Multicomponent Nonlinear Systems of Bose-Fermi Fields: Exact Solutions

2011 ◽  
Author(s):  
Nikolay A. Kostov ◽  
Vladimir S. Gerdjikov ◽  
Tihomir I. Valchev
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions

scholarly journals Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yongyi Gu ◽  
Fanning Meng
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions ◽  
Rational Function ◽  
Analytical Solutions ◽  
Direct Methods ◽  
Expansion Method ◽  
Complex Method ◽  
Kp Equation ◽  
Extended Complex ◽  
Complex Nonlinear Systems

In this paper, we derive analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation by two different systematic methods. Using the exp⁡(-ψ(z))-expansion method, exact solutions of the mentioned equation including hyperbolic, exponential, trigonometric, and rational function solutions have been obtained. Based on the work of Yuan et al., we proposed the extended complex method to seek exact solutions of the (2+1)-dimensional KP equation. The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.

scholarly journals Meromorphic exact solutions of the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1342-1351
Author(s):  
Najva Aminakbari ◽  
Yongyi Gu ◽  
Wenjun Yuan
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions ◽  
Elliptic Function ◽  
Traveling Wave ◽  
Complex Method ◽  
Soliton Equation ◽  
Dynamic Behaviors ◽  
Complex Nonlinear Systems

Abstract In this article, meromorphic exact solutions for the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff (gCBS) equation are obtained by using the complex method. With the applications of our results, traveling wave exact solutions of the breaking soliton equation are achieved. The dynamic behaviors of exact solutions of the (2 + 1)-dimensional gCBS equation are shown by some graphs. In particular, the graphs of elliptic function solutions are comparatively rare in other literature. The idea of this study can be applied to the complex nonlinear systems of some areas of engineering.

Truncated Painlevé Expansion – A Unified Approach to Exact Solutions and Dromion Interactions of (2+1)-Dimensional Nonlinear Systems

2007 ◽  
Vol 62 (3-4) ◽  
pp. 107-116 ◽  
Author(s):  
Ramaswamy Radha ◽  
Xiao Yan Tang ◽  
Sen Yue Lou
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions ◽  
Painlevé Analysis ◽  
Unified Approach ◽  
Different Types ◽  
Painleve Analysis ◽  
Truncated Painlevé Expansion

In this paper, we formulate a method wherein we harness the results of the Painlevé analysis to generate the solutions of the (2+1)-dimensional Ablowitz-Kaup-Newell-Segur system completely in terms of the arbitrary functions. This method is mainly based on the results of the truncated Painlevé expansion. Different types of interactions among dromions are deeply understood both analytically and numerically. Especially, different from the traditional viewpoint, we point out that the soliton (dromion) fission and fusion may be an approximate phenomenon.

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