Periodic and solitary wave solutions of coupled nonlinear wave equations using the first integral method

2012 ◽  
Vol 85 (6) ◽  
pp. 065003 ◽  
Author(s):  
Ahmet Bekir ◽  
Ömer Ünsal
Keyword(s):  
Solitary Wave ◽  
Nonlinear Wave ◽  
Integral Method ◽  
Wave Equations ◽  
First Integral ◽  
Nonlinear Wave Equations ◽  
Solitary Wave Solutions ◽  
First Integral Method ◽  
Wave Solutions

scholarly journals Solitary and Periodic Wave Solutions of Sasa–Satsuma Equation and Their Relationship with Hamilton Energy

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Weiguo Zhang ◽  
Xingqian Ling ◽  
Bei-Bei Wang ◽  
Shaowei Li
Keyword(s):  
Solitary Wave ◽  
Integral Method ◽  
First Integral ◽  
Periodic Wave ◽  
Evolutionary Relationships ◽  
Solitary Wave Solutions ◽  
First Integral Method ◽  
Periodic Wave Solutions ◽  
Hamilton Energy ◽  
Wave Solutions

In this paper, we study the exact solitary wave solutions and periodic wave solutions of the S-S equation and give the relationships between solutions and the Hamilton energy of their amplitudes. First, on the basis of the theory of dynamical system, we make qualitative analysis on the amplitudes of solutions. Then, by using undetermined hypothesis method, the first integral method, and the appropriate transformation, two bell-shaped solitary wave solutions and six exact periodic wave solutions are obtained. Furthermore, we discuss the evolutionary relationships between these solutions and find that the appearance of these solutions for the S-S equation is essentially determined by the value which the Hamilton energy takes. Finally, we give some diagrams which show the changing process from the periodic wave solutions to the solitary wave solutions when the Hamilton energy changes.

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 The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yadong Shang ◽  
Xiaoxiao Zheng
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Elliptic Function ◽  
Integral Method ◽  
First Integral ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
First Integral Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions

This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type fornandE, the solitary wave solutions of kink-type forEand bell-type forn, the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.

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