EXPLICIT AND EXACT SOLUTIONS TO THE mKdV-SINE-GORDON EQUATION

2008 ◽  
Vol 22 (15) ◽  
pp. 1471-1485 ◽  
Author(s):  
YUANXI XIE
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Variable Separation ◽  
Sine Gordon Equation ◽  
Simple Manner

By introducing an auxiliary ordinary differential equation and solving it by the method of variable separation, rich types of explicit and exact solutions of the mKdV-sine-Gordon equation are presented in a simple manner.

EXPLICIT EXACT SOLUTIONS TO THE (2+1) DIMENSIONAL SINH-POISSON EQUATION

2010 ◽  
Vol 24 (17) ◽  
pp. 3395-3409
Author(s):  
YUANXI XIE ◽  
SHIYU PENG
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Exact Solutions ◽  
Poisson Equation ◽  
Variable Separation ◽  
Simple Manner

By introducing an auxiliary ordinary differential equation and solving it by the method of variable separation, many explicit exact solutions of the (2+1) dimensional sinh-Poisson equation are presented in a simple manner.

scholarly journals The Cauchy Problem for the Generalized Hyperbolic Novikov–Veselov Equation via the Moutard Symmetries

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2113
Author(s):  
Alla A. Yurova ◽  
Artyom V. Yurov ◽  
Valerian A. Yurov
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Cauchy Problem ◽  
Exact Solutions ◽  
Airy Function ◽  
The Real ◽  
The Cauchy Problem

We begin by introducing a new procedure for construction of the exact solutions to Cauchy problem of the real-valued (hyperbolic) Novikov–Veselov equation which is based on the Moutard symmetry. The procedure shown therein utilizes the well-known Airy function Ai(ξ) which in turn serves as a solution to the ordinary differential equation d2zdξ2=ξz. In the second part of the article we show that the aforementioned procedure can also work for the n-th order generalizations of the Novikov–Veselov equation, provided that one replaces the Airy function with the appropriate solution of the ordinary differential equation dn−1zdξn−1=ξz.

scholarly journals Exact solutions to the sine-Gordon equation

2010 ◽  
Vol 51 (12) ◽  
pp. 123521 ◽  
Author(s):  
Tuncay Aktosun ◽  
Francesco Demontis ◽  
Cornelis van der Mee
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Sine Gordon Equation
Sign in / Sign up

Export Citation Format

Share Document