Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmet...Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmetric solitons upon assigning appropriate values to some parameters.Furthermore,a double-peaked lump solution can be constructed with breather degeneration approach.By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions,various kinds of interactional structures are constructed;There include the soliton molecule(SM),the breather molecule(BM)and the soliton-breather molecule(SBM).Graphical investigation and theoretical analysis show that the interactions composed of SM,BM and SBM are inelastic.展开更多
With the aid of the Painlevé analysis, we obtain residual symmetries for a new(3+1)-dimensional generalized Kadomtsev–Petviashvili(gKP) equation. The residual symmetry is localized and the finite transformation ...With the aid of the Painlevé analysis, we obtain residual symmetries for a new(3+1)-dimensional generalized Kadomtsev–Petviashvili(gKP) equation. The residual symmetry is localized and the finite transformation is proposed by introducing suitable auxiliary variables. In addition, the interaction solutions of the(3+1)-dimensional gKP equation are constructed via the consistent Riccati expansion method. Particularly, some analytical soliton-cnoidal interaction solutions are discussed in graphical way.展开更多
The quantum hydrodynamic model for ion-acoustic waves in plasmas is studied.First,we design a new disturbance expansion to describe the ion fluid velocity and electric field potential.It should be emphasized that the ...The quantum hydrodynamic model for ion-acoustic waves in plasmas is studied.First,we design a new disturbance expansion to describe the ion fluid velocity and electric field potential.It should be emphasized that the piecewise function perturbation form is new with great difference from the previous perturbation.Then,based on the piecewise function perturbation,a(3+1)-dimensional generalized modified Korteweg–de Vries Zakharov–Kuznetsov(mKdV-ZK)equation is derived for the first time,which is an extended form of the classical mKdV equation and the ZK equation.The(3+1)-dimensional generalized time-space fractional mKdV-ZK equation is constructed using the semi-inverse method and the fractional variational principle.Obviously,it is more accurate to depict some complex plasma processes and phenomena.Further,the conservation laws of the generalized time-space fractional mKdV-ZK equation are discussed.Finally,using the multi-exponential function method,the non-resonant multiwave solutions are constructed,and the characteristics of ion-acoustic waves are well described.展开更多
Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coeffi...Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions(or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.展开更多
The symmetries and the exact solutions of the （3＋l）-dimensional nonlinear incompressible non-hydrostatic Boussi- nesq （INHB） equations, which describe atmospheric gravity waves, are studied in this paper. The cal...The symmetries and the exact solutions of the （3＋l）-dimensional nonlinear incompressible non-hydrostatic Boussi- nesq （INHB） equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the （3＋ 1）-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the （3＋1）-dimensional INHB system.展开更多
In this paper, the（2＋1）-dimensional perturbed Boussinesq equation is transformed into a series of two-dimensional（2 D） similarity reduction equations by using the approximate symmetry method. A step-by-step proce...In this paper, the（2＋1）-dimensional perturbed Boussinesq equation is transformed into a series of two-dimensional（2 D） similarity reduction equations by using the approximate symmetry method. A step-by-step procedure is used to acquire Jacobi elliptic function solutions to these similarity equations, which generate the truncated series solutions to the original perturbed Boussinesq equation. Aside from some singular area, the series solutions are convergent when the perturbation parameter is diminished.展开更多
Based on a 2 × 2 eigenvalue problem,a set of（1 ＋ 1）-dimensional soliton equations are proposed.Moreover,we obtain a finite dimensional Hamilton system with the help of nonlinearization approach.Then the genera...Based on a 2 × 2 eigenvalue problem,a set of（1 ＋ 1）-dimensional soliton equations are proposed.Moreover,we obtain a finite dimensional Hamilton system with the help of nonlinearization approach.Then the generating function approach and the way to straighten out of Fm-flow are used to prove the involutivity and the functional independence of conserved integrals for the finite-dimensional Hamilton system,hence,we can verify it is completely integrable in Liouville sense.展开更多
A new idea is put forward to modify the Clarkson-Kruskal （CK） direct method. Using the usual CK direct method to a coupled KdV system, two types of usual similarity reductions can be obtained. However, the applicati...A new idea is put forward to modify the Clarkson-Kruskal （CK） direct method. Using the usual CK direct method to a coupled KdV system, two types of usual similarity reductions can be obtained. However, the application of the modified CK direct method leads to three types of new similarity reductions different from the usual ones.展开更多
基金Supported by the National Natural Science Foundation of China(12001424)the Natural Science Basic Research Program of Shaanxi Province(2021JZ-21)the Fundamental Research Funds for the Central Universities(2020CBLY013)。
文摘Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmetric solitons upon assigning appropriate values to some parameters.Furthermore,a double-peaked lump solution can be constructed with breather degeneration approach.By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions,various kinds of interactional structures are constructed;There include the soliton molecule(SM),the breather molecule(BM)and the soliton-breather molecule(SBM).Graphical investigation and theoretical analysis show that the interactions composed of SM,BM and SBM are inelastic.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11835011 and 12074343)。
文摘With the aid of the Painlevé analysis, we obtain residual symmetries for a new(3+1)-dimensional generalized Kadomtsev–Petviashvili(gKP) equation. The residual symmetry is localized and the finite transformation is proposed by introducing suitable auxiliary variables. In addition, the interaction solutions of the(3+1)-dimensional gKP equation are constructed via the consistent Riccati expansion method. Particularly, some analytical soliton-cnoidal interaction solutions are discussed in graphical way.
基金Project supported by the National Natural Science Foundation of China(Grant No.11975143)the Natural Science Foundation of Shandong Province of China(Grant No.ZR2018MA017)+1 种基金the Taishan Scholars Program of Shandong Province,China(Grant No.ts20190936)the Shandong University of Science and Technology Research Fund(Grant No.2015TDJH102).
文摘The quantum hydrodynamic model for ion-acoustic waves in plasmas is studied.First,we design a new disturbance expansion to describe the ion fluid velocity and electric field potential.It should be emphasized that the piecewise function perturbation form is new with great difference from the previous perturbation.Then,based on the piecewise function perturbation,a(3+1)-dimensional generalized modified Korteweg–de Vries Zakharov–Kuznetsov(mKdV-ZK)equation is derived for the first time,which is an extended form of the classical mKdV equation and the ZK equation.The(3+1)-dimensional generalized time-space fractional mKdV-ZK equation is constructed using the semi-inverse method and the fractional variational principle.Obviously,it is more accurate to depict some complex plasma processes and phenomena.Further,the conservation laws of the generalized time-space fractional mKdV-ZK equation are discussed.Finally,using the multi-exponential function method,the non-resonant multiwave solutions are constructed,and the characteristics of ion-acoustic waves are well described.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11505154,11605156,11775146,and 11975204)the Zhejiang Provincial Natural Science Foundation of China(Grant Nos.LQ16A010003 and LY19A050003)+5 种基金the China Scholarship Council(Grant No.201708330479)the Foundation for Doctoral Program of Zhejiang Ocean University(Grant No.Q1511)the Natural Science Foundation(Grant No.DMS-1664561)the Distinguished Professorships by Shanghai University of Electric Power(China)North-West University(South Africa)King Abdulaziz University(Saudi Arabia)
文摘Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions(or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.
基金Project supported by the Natural Science Foundation of Guangdong Province, China (Grant Nos. 10452840301004616 and S2011040000403)the National Natural Science Foundation of China (Grant No. 41176005)the Science and Technology Project Foundation of Zhongshan, China (Grnat No. 20123A326)
文摘The symmetries and the exact solutions of the （3＋l）-dimensional nonlinear incompressible non-hydrostatic Boussi- nesq （INHB） equations, which describe atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the （3＋ 1）-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the （3＋1）-dimensional INHB system.
基金Project supported by the National Natural Science Foundation of China(Grant No.11505094)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20150984)
文摘In this paper, the（2＋1）-dimensional perturbed Boussinesq equation is transformed into a series of two-dimensional（2 D） similarity reduction equations by using the approximate symmetry method. A step-by-step procedure is used to acquire Jacobi elliptic function solutions to these similarity equations, which generate the truncated series solutions to the original perturbed Boussinesq equation. Aside from some singular area, the series solutions are convergent when the perturbation parameter is diminished.
文摘Based on a 2 × 2 eigenvalue problem,a set of（1 ＋ 1）-dimensional soliton equations are proposed.Moreover,we obtain a finite dimensional Hamilton system with the help of nonlinearization approach.Then the generating function approach and the way to straighten out of Fm-flow are used to prove the involutivity and the functional independence of conserved integrals for the finite-dimensional Hamilton system,hence,we can verify it is completely integrable in Liouville sense.
文摘A new idea is put forward to modify the Clarkson-Kruskal （CK） direct method. Using the usual CK direct method to a coupled KdV system, two types of usual similarity reductions can be obtained. However, the application of the modified CK direct method leads to three types of new similarity reductions different from the usual ones.
基金Supported by the National Natural Science Foundation of Education Depart ment of HenanProvince of China (2006110002) ,the Science Foundation of Henan University of Science and Technology(2004ZD002 ,2006ZY001)
