The generalizing Riccati equation mapping method in non-linear evolution equation: application to (2+1)-dimensional Boiti–Leon–Pempinelle equation

2008 ◽  
Vol 37 (5) ◽  
pp. 1335-1342 ◽  
Author(s):  
Shun-dong Zhu
Keyword(s):  
Evolution Equation ◽  
Riccati Equation ◽  
Mapping Method ◽  
Linear Evolution ◽  
Linear Evolution Equation ◽  
Non Linear

Modified dissipativity for a non-linear evolution equation arising in turbulence

1979 ◽  
Vol 71 (3) ◽  
pp. 237-256 ◽  
Author(s):  
C. Bardos ◽  
P. Penel ◽  
U. Frisch ◽  
P. L. Sulem
Keyword(s):  
Evolution Equation ◽  
Linear Evolution ◽  
Linear Evolution Equation ◽  
Non Linear

scholarly journals Double Reduction Analysis of Benjamin, DGH and Generalized DGH Equations

2020 ◽  
Vol Volume 14 ◽  
Keyword(s):  
Evolution Equation ◽  
Exact Solutions ◽  
Higher Order ◽  
Reduction Theory ◽  
Double Reduction ◽  
Linear Evolution ◽  
Holm Equation ◽  
Linear Evolution Equation ◽  
Non Linear ◽  
Benjamin Equation

The exact solutions of non-linear evolution equation, Benjamin equation, Dullin-Gottwald-Holm (DGH) equation and generalized Dullin-Gottwald-Holm equation are established using the conserved vectors. The multiplier approach is applied to construct the conserved vectors for equations under consideration. For non-linear evolution equation three conserved vectors and for Benjamin equation four conserved vectors are obtained. The conserved vectors for DGH and generalized DGH equations were reported in [1]. The higher order multiplier is considered for DGH equation and a new conserved vector is found. The double reduction theory is utilized to obtain various exact solutions for Benjamin equation, DGH equation and generalized DGH equation.

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