scholarly journals The Cauchy Problem and Stability of Solitary-Wave Solutions for RLW–KP-Type Equations

2002 ◽  
Vol 185 (2) ◽  
pp. 437-482 ◽  
Author(s):  
Jerry L. Bona ◽  
Yue Liu ◽  
Michael M. Tom
Keyword(s):  
Cauchy Problem ◽  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
The Cauchy Problem

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.

scholarly journals Wave-Breaking Phenomena and Existence of Peakons for a Generalized Compressible Elastic-Rod Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xiaolian Ai ◽  
Lingyu Jiang ◽  
Ting Yi
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Wave Breaking ◽  
Strong Solutions ◽  
Solitary Wave Solutions ◽  
Elastic Rod ◽  
Wave Solutions ◽  
The Cauchy Problem ◽  
Breaking Mechanism ◽  
Rod Equation

Consideration in this paper is the Cauchy problem of a generalized hyperelastic-rod wave equation. We first derive a wave-breaking mechanism for strong solutions, which occurs in finite time for certain initial profiles. In addition, we determine the existence of some new peaked solitary wave solutions.

scholarly journals Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 896-909 ◽  
Author(s):  
Dianchen Lu ◽  
Aly R. Seadawy ◽  
Mujahid Iqbal
Keyword(s):  
Solitary Wave ◽  
Nonlinear Partial Differential Equations ◽  
Research Work ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Mapping Method ◽  
New Method ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

AbstractIn this research work, for the first time we introduced and described the new method, which is modified extended auxiliary equation mapping method. We investigated the new exact traveling and families of solitary wave solutions of two well-known nonlinear evaluation equations, which are generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified forms of Camassa-Holm equations. We used a new technique and we successfully obtained the new families of solitary wave solutions. As a result, these new solutions are obtained in the form of elliptic functions, trigonometric functions, kink and antikink solitons, bright and dark solitons, periodic solitary wave and traveling wave solutions. These new solutions show the power and fruitfulness of this new method. We can solve other nonlinear partial differential equations with the use of this method.

Solitary wave solutions to a system of Boussinesq-like equations

1992 ◽  
Vol 2 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Peter L. Christiansen ◽  
Virginia Muto ◽  
Salvatore Rionero
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions
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