Exact Solutions to Nonlinear Equations and Systems of Equations of General Form in Mathematical Physics

2008 ◽  
Author(s):  
A. D. Polyanin ◽  
A. I. Zhurov ◽  
E. A. Vyazmina ◽  
Michail D. Todorov
Keyword(s):  
Exact Solutions ◽  
Nonlinear Equations ◽  
Mathematical Physics ◽  
Systems Of Equations ◽  
Nonlinear Equations And Systems

scholarly journals On one method for constructing exact solutions of nonlinear equations of mathematical physics

2019 ◽  
Vol 489 (3) ◽  
pp. 235-239
Author(s):  
A. D. Polyanin ◽  
A. I. Zhurov
Keyword(s):  
Exact Solutions ◽  
Nonlinear Equations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Mathematical Physics ◽  
Integral Type ◽  
Diffusion Type ◽  
Wave Solutions ◽  
Equations Of Mathematical Physics

A new method for constructing exact solutions of nonlinear equations of mathematical physics, which is based on nonlinear integral type transformations in combination with the splitting principle, is proposed. The effectiveness of the method is illustrated on nonlinear equations of the reaction-diffusion type, which depend on two or three arbitrary functions. New exact functional separable solutions and generalized traveling wave solutions are described.

scholarly journals ON NONLINEARITY OF p-BRANE DYNAMICS

2012 ◽  
Vol 09 (06) ◽  
pp. 1261017 ◽  
Author(s):  
A. A. ZHELTUKHIN
Keyword(s):  
Exact Solutions ◽  
Minkowski Space ◽  
Nonlinear Equations ◽  
New Exact Solutions ◽  
Dimensional Minkowski Space

Nonlinear equations of p-branes in D = (2p + 1)-dimensional Minkowski space are discussed. Presented are new exact solutions for a set of spinning p-branes with the Abelian symmetries U(1) × U(1) × ⋯ ×U(1) of their shapes.

scholarly journals New Jacobi Elliptic Function Solutions for the Zakharov Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yun-Mei Zhao
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function

A generalized(G′/G)-expansion method is proposed to seek the exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the Zakharov equations. As a result, some new Jacobi elliptic function solutions of the Zakharov equations are obtained. This method can also be applied to other nonlinear evolution equations in mathematical physics.

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