New Travelling Solitary Wave and Periodic Solutions of the Generalized Kawahara Equation

2007 ◽  
Author(s):  
Huaitang Chen ◽  
Huicheng Yin ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Solitary Wave ◽  
Periodic Solutions ◽  
Kawahara Equation

scholarly journals Study on New Doubly-periodic Solutions of two Coupled Nonlinear Wave Equations in Complex and Real Fields

2004 ◽  
Vol 59 (1-2) ◽  
pp. 29-34 ◽  
Author(s):  
Zhenya Yan
Keyword(s):  
Solitary Wave ◽  
Periodic Solutions ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Scalar Fields ◽  
Nonlinear Wave Equations ◽  
Solitary Wave Solutions ◽  
Real Scalar ◽  
Wave Solutions

In this paper, new doubly-periodic solutions in terms of Weierstrass elliptic functions are investigated for the coupled nonlinear Schr¨odinger equation and systems of two coupled real scalar fields. Solitary wave solutions are also given as simple limits of doubly periodic solutions. - PACS: 03.40.Kf; 02.30Ik

scholarly journals Solitary-Wave and Periodic Solutions of the Kuramoto-Velarde Dispersive Equation

2016 ◽  
Vol 46 (3) ◽  
pp. 65-74 ◽  
Author(s):  
Ognyan Y. Kamenov
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Solitary Waves ◽  
Transformation Method ◽  
Dispersive Equation ◽  
Bilinear Transformation ◽  
Mapping Approach ◽  
Solitary Solutions

Abstract In the present paper, solitary solutions of the Kuramoto- Velarde (K-V) dispersive equation have been found, using the deformation and mapping approach. These exact solutions show the dynamics and the evolution of dispersive solitary waves. In the case α2 = α3, three families of exact periodic solutions have been obtained by employing the bilinear transformation method.

scholarly journals On Solitary Wave Solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara Equations with the Dual-Power Law Nonlinearities

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Nattakorn Sukantamala ◽  
Supawan Nanta
Keyword(s):  
Solitary Wave ◽  
Nonlinear Wave ◽  
Traveling Wave ◽  
Analytic Solution ◽  
Traveling Wave Solutions ◽  
Well Posedness ◽  
Solitary Wave Solutions ◽  
Kawahara Equation ◽  
Ansatz Method ◽  
Wave Solutions

The nonlinear wave equation is a significant concern to describe wave behavior and structures. Various mathematical models related to the wave phenomenon have been introduced and extensively being studied due to the complexity of wave behaviors. In the present work, a mathematical model to obtain the solution of the nonlinear wave by coupling the classical Camassa-Holm equation and the Rosenau-RLW-Kawahara equation with the dual term of nonlinearities is proposed. The solution properties are analytically derived. The new model still satisfies the fundamental energy conservative property as the original models. We then apply the energy method to prove the well-posedness of the model under the solitary wave hypothesis. Some categories of exact solitary wave solutions of the model are described by using the Ansatz method. In addition, we found that the dual term of nonlinearity is essential to obtain the class of analytic solution. Besides, we provide some graphical representations to illustrate the behavior of the traveling wave solutions.

Exact single travelling wave solutions to the fractional perturbed Gerdjikov–Ivanov equation in nonlinear optics

2021 ◽  
pp. 2150377
Author(s):  
Xiang Xiao ◽  
Zhixiang Yin
Keyword(s):  
Solitary Wave ◽  
Periodic Solutions ◽  
Travelling Wave ◽  
Polynomial Method ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Trial Equation Method ◽  
Wave Solutions ◽  
Triangular Function ◽  
Almost All

In this paper, exact single travelling wave solutions to the nonlinear fractional perturbed Gerdjikov–Ivanov equation are captured by the complete discrimination system for polynomial method and the trial equation method. In the classification, we can find out the original equation has rational function solutions, solitary wave solutions, triangular function periodic solutions, and elliptic function periodic solutions, which are normally very difficult to be obtained by other methods. In particular, the concrete parameters are set to show that the solutions in the classification can be realized in almost all cases.

scholarly journals Steady Solitary and Periodic Waves in a Nonlinear Nonintegrable Lattice

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1608
Author(s):  
Igor Andrianov ◽  
Aleksandr Zemlyanukhin ◽  
Andrey Bochkarev ◽  
Vladimir Erofeev
Keyword(s):  
Numerical Simulation ◽  
Solitary Wave ◽  
Periodic Solutions ◽  
Initial Conditions ◽  
Periodic Waves ◽  
Two Stage ◽  
Second Stage ◽  
Ostrovsky Equation ◽  
Discrete Analogs

In this paper, stationary solitary and periodic waves of a nonlinear nonintegrable lattice are numerically constructed using a two-stage approach. First, as a result of continualization, a nonintegrable generalized Boussinesq—Ostrovsky equation is obtained, for which the solitary-wave and periodic solutions are numerically found by the Petviashvili method. In the second stage, discrete analogs of the obtained solutions are used as initial conditions in the numerical simulation of the original lattice. It is shown that the initial perturbations constructed in this way propagate along the lattice without changing their shape.

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