scholarly journals Plenty accurate soliton wave solutions of the prototype of an excitable system

AIP Advances ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 095315
Author(s):  
S. H. Alfalqi ◽  
J. F. Alzaidi ◽  
Ying-Fang Zhang ◽  
Samir A. Salama ◽  
Mostafa M. A. Khater
Keyword(s):  
Excitable System ◽  
Wave Solutions ◽  
Soliton Wave Solutions

Analytical new soliton wave solutions of the nonlinear conformable time-fractional coupled Whitham–Broer–Kaup equations

2021 ◽  
pp. 2150492
Author(s):  
Delmar Sherriffe ◽  
Diptiranjan Behera ◽  
P. Nagarani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Function Method ◽  
Visual Representations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Varying Parameters ◽  
Wave Solutions ◽  
Soliton Wave Solutions

The study of nonlinear physical and abstract systems is greatly important in order to determine the behavior of the solutions for Fractional Partial Differential Equations (FPDEs). In this paper, we study the analytical wave solutions of the time-fractional coupled Whitham–Broer–Kaup (WBK) equations under the meaning of conformal fractional derivative. These solutions are derived using the modified extended tanh-function method. Accordingly, different new forms of the solutions are obtained. In order to understand its behavior under varying parameters, we give the visual representations of all the solutions. Finally, the graphs are discussed and a conclusion is given.

Multiple rogue and soliton wave solutions to the generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation arising in fluid mechanics and plasma physics

2021 ◽  
pp. 2150383
Author(s):  
Onur Alp Ilhan ◽  
Sadiq Taha Abdulazeez ◽  
Jalil Manafian ◽  
Hooshmand Azizi ◽  
Subhiya M. Zeynalli
Keyword(s):  
Rogue Wave ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
The Novel ◽  
Algebraic Equations ◽  
Bilinear Method ◽  
Dynamical Characteristics ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Soliton Wave Solutions

Under investigation in this paper is the generalized Konopelchenko–Dubrovsky–Kaup-Kupershmidt equation. Based on bilinear method, the multiple rogue wave (RW) solutions and the novel multiple soliton solutions are constructed by giving some specific activation functions for the considered model. By means of symbolic computation, these analytical solutions and corresponding rogue wave solutions are obtained via Maple 18 software. The exact lump and RW solutions, by solving the under-determined nonlinear system of algebraic equations for the specified parameters, will be constructed. Via various three-dimensional plots and density plots, dynamical characteristics of these waves are exhibited.

Lump soliton wave solutions for the (2+1)-dimensional Konopelchenko–Dubrovsky equation and KdV equation

2019 ◽  
Vol 33 (18) ◽  
pp. 1950199 ◽  
Author(s):  
Mostafa M. A. Khater ◽  
Dianchen Lu ◽  
Raghda A. M. Attia
Keyword(s):  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Auxiliary Equation ◽  
Wave Solutions ◽  
All Solutions ◽  
Long Range Interactions ◽  
Weak Scattering ◽  
Novel Method ◽  
Soliton Wave Solutions

This paper studies (2+1)-dimensional Konopelchenko–Dubrovsky equation and (2+1)-dimensional KdV equation via a modified auxiliary equation technique. These two systems describe the connection between the nonlinear weaves with a weak scattering and long-range interactions between the tropical, mid-latitude troposphere, the interaction of equatorial and mid-latitude Rossby waves, respectively. We implement a novel technique to these systems to find analytical traveling wave solutions. The performance of this novel method shows its ability for applying on various nonlinear partial differential equations. All solutions obtained are checked by the Maple software system and verified for its high fidelity.

Soliton wave solutions in optical metamaterials with anti-cubic law of nonlinearity by ITEM

Optik ◽  
2018 ◽  
Vol 164 ◽  
pp. 371-379 ◽  
Author(s):  
Mohammadreza Foroutan ◽  
Jalil Manafian ◽  
Isa Zamanpour
Keyword(s):  
Optical Metamaterials ◽  
Wave Solutions ◽  
Cubic Law ◽  
Soliton Wave Solutions

scholarly journals Traveling wave solutions for (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity

2019 ◽  
Vol 8 (1) ◽  
pp. 559-567 ◽  
Author(s):  
M.S. Osman ◽  
Hadi Rezazadeh ◽  
Mostafa Eslami
Keyword(s):  
Applied Sciences ◽  
Power Law ◽  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Mathematical Tool ◽  
Rational Solutions ◽  
Wave Solutions ◽  
The Unified Method ◽  
Soliton Wave Solutions ◽  
Unified Method

Abstract In this work, we consider the (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity. Solitary wave solutions, soliton wave solutions, elliptic wave solutions, and periodic (hyperbolic) wave rational solutions are obtained by means of the unified method. The solutions showed that this method provides us with a powerful mathematical tool for solving nonlinear conformable fractional evolution equations in various fields of applied sciences.

Multi and breather wave soliton solutions and the linear superposition principle for generalized Hietarinta equation

2022 ◽  
Author(s):  
S. Şule Şener Kiliç
Keyword(s):  
Asymptotic Behavior ◽  
Superposition Principle ◽  
Soliton Solutions ◽  
Asymptotic Behavior Of Solutions ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Linear Superposition ◽  
Wave Solutions ◽  
Linear Superposition Principle ◽  
Soliton Wave Solutions

In this paper, we study the generalized ([Formula: see text])-dimensional Hietarinta equation which is investigated by utilizing Hirota’s bilinear method. Also, the bilinear form is obtained, and the N-soliton solutions are constructed. In addition, multi-wave and breather wave solutions of the addressed equation with specific coefficients are presented. Finally, under certain conditions, the asymptotic behavior of solutions is analyzed in both methods. Moreover, we employ the linear superposition principle to determine [Formula: see text]-soliton wave solutions for the generalized ([Formula: see text])-dimensional Hietarinta equation.

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