scholarly journals Conservation laws and line soliton solutions of a family of modified KP equations

2020 ◽  
Vol 13 (10) ◽  
pp. 2655-2665 ◽  
Author(s):  
Stephen C. Anco ◽  
◽  
Maria Luz Gandarias ◽  
Elena Recio ◽  
Keyword(s):  
Conservation Laws ◽  
Soliton Solutions ◽  
Kp Equations ◽  
Line Soliton

scholarly journals Lie Symmetries and Low-Order Conservation Laws of a Family of Zakharov-Kuznetsov Equations in 2 + 1 Dimensions

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1277
Author(s):  
María S. Bruzón ◽  
Tamara M. Garrido ◽  
Elena Recio ◽  
Rafael de la Rosa
Keyword(s):  
Conservation Laws ◽  
Hamiltonian Formulation ◽  
Soliton Solutions ◽  
Lie Symmetry ◽  
Lie Symmetries ◽  
Point Of View ◽  
Variational Structure ◽  
Potential Form ◽  
Line Soliton ◽  
Low Order

In this work, we study a generalised (2+1) equation of the Zakharov–Kuznetsov (ZK)(m,n,k) equation involving three arbitrary functions. From the point of view of the Lie symmetry theory, we have derived all Lie symmetries of this equation depending on the arbitrary functions. Line soliton solutions have also been obtained. Moreover, we study the low-order conservation laws by applying the multiplier method. This family of equations is rich in Lie symmetries and conservation laws. Finally, when the equation is expressed in potential form, it admits a variational structure in the case when two of the arbitrary functions are linear. In addition, the corresponding Hamiltonian formulation is presented.

N-soliton solutions and localized wave interaction solutions of a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyamaf equation

2021 ◽  
pp. 2150277
Author(s):  
Hongcai Ma ◽  
Qiaoxin Cheng ◽  
Aiping Deng
Keyword(s):  
Dynamic Behavior ◽  
Soliton Solution ◽  
Soliton Solutions ◽  
Wave Interaction ◽  
Bilinear Transformation ◽  
Interaction Solution ◽  
Interaction Solutions ◽  
Ytsf Equation ◽  
Line Soliton

[Formula: see text]-soliton solutions are derived for a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by using bilinear transformation. Some local waves such as period soliton, line soliton, lump soliton and their interaction are constructed by selecting specific parameters on the multi-soliton solutions. By selecting special constraints on the two soliton solutions, period and lump soliton solution can be obtained; three solitons can reduce to the interaction solution between period soliton and line soliton or lump soliton and line soliton under special parameters; the interaction solution among period soliton and two line solitons, or the interaction solution for two period solitons or two lump solitons via taking specific constraints from four soliton solutions. Finally, some images of the results are drawn, and their dynamic behavior is analyzed.

Extended KP equations and extended system of KP equations: multiple-soliton solutions

2011 ◽  
Vol 89 (7) ◽  
pp. 739-743 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Dispersion Relations ◽  
Kp Equation ◽  
Extended System ◽  
Multiple Soliton Solutions ◽  
Simplified Method ◽  
Kp Equations

In this work we study an extended Kadomtsev–Petviashvili (KP) equation and a system of KP equations. We show that the extension terms do not kill the integrability of typical models. Hereman’s simplified method is used to justify this goal. Multiple soliton solutions will be derived for each model. The analysis highlights the effects of the extension terms on the dispersion relations, and hence on the structures of the solutions.

Sign in / Sign up

Export Citation Format

Share Document