scholarly journals Stability of traveling wave solutions to Cauchy problem of diagnolizable quasilinear hyperbolic systems

2014 ◽  
Vol 34 (11) ◽  
pp. 4735-4749 ◽  
Author(s):  
Cunming Liu ◽  
Jianli Liu
Keyword(s):  
Cauchy Problem ◽  
Traveling Wave ◽  
Hyperbolic Systems ◽  
Traveling Wave Solutions ◽  
Quasilinear Hyperbolic Systems ◽  
Wave Solutions

scholarly journals Remarks on solitary waves and Cauchy problem for Half-wave-Schrödinger equations

2020 ◽  
pp. 2050058
Author(s):  
Yakine Bahri ◽  
Slim Ibrahim ◽  
Hiroaki Kikuchi
Keyword(s):  
Cauchy Problem ◽  
Traveling Wave ◽  
Critical Case ◽  
Orbital Stability ◽  
Traveling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Half Wave ◽  
The Cauchy Problem ◽  
Interesting Open Problem

In this paper, we study solitary wave solutions of the Cauchy problem for Half-wave-Schrödinger equation in the plane. First, we show the existence and the orbital stability of the ground states. Second, we prove that given any speed [Formula: see text], traveling wave solutions exist and converge to the zero wave as the velocity tends to [Formula: see text]. Finally, we solve the Cauchy problem for initial data in [Formula: see text], with [Formula: see text]. The critical case [Formula: see text] still stands as an interesting open problem.

Traveling wave solutions of the one-dimensional Boussinesq paradigm equation

2013 ◽  
Author(s):  
V. M. Vassilev ◽  
P. A. Djondjorov ◽  
M. Ts. Hadzhilazova ◽  
I. M. Mladenov
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
One Dimensional ◽  
Wave Solutions ◽  
The One

scholarly journals Lie Group Method for Solving the Negative-Order Kadomtsev–Petviashvili Equation (nKP)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 224
Author(s):  
Ghaylen Laouini ◽  
Amr M. Amin ◽  
Mohamed Moustafa
Keyword(s):  
Lie Group ◽  
Traveling Wave ◽  
Invariant Solution ◽  
Traveling Wave Solutions ◽  
Group Method ◽  
Lie Group Method ◽  
Reduced Equations ◽  
Wave Solutions ◽  
Negative Order ◽  
Petviashvili Equation

A comprehensive study of the negative-order Kadomtsev–Petviashvili (nKP) partial differential equation by Lie group method has been presented. Initially the infinitesimal generators and symmetry reduction, which were obtained by applying the Lie group method on the negative-order Kadomtsev–Petviashvili equation, have been used for constructing the reduced equations. In particular, the traveling wave solutions for the negative-order KP equation have been derived from the reduced equations as an invariant solution. Finally, the extended improved (G′/G) method and the extended tanh method are described and applied in constructing new explicit expressions for the traveling wave solutions. Many new and more general exact solutions are obtained.

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