Solution by the spectral-transform method of a nonlinear evolution equation including as a special case the cylindrical KdV equation

1978 ◽  
Vol 23 (4) ◽  
pp. 150-154 ◽  
Author(s):  
F. Calogero ◽  
A. Degasperis
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Transform Method ◽  
Spectral Transform ◽  
Special Case

scholarly journals Bäcklund Transformations between the KdV Equation and a New Nonlinear Evolution Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Xifang Cao
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
The Other ◽  
Bäcklund Transformations ◽  
Backlund Transformations ◽  
The Kdv Equation ◽  
New Equation

We first give a Bäcklund transformation from the KdV equation to a new nonlinear evolution equation. We then derive two Bäcklund transformations with two pseudopotentials, one of which is from the KdV equation to the new equation and the other from the new equation to itself. As applications, by applying our Bäcklund transformations to known solutions, we construct some novel solutions to the new equation.

scholarly journals On nonlinear evolution equation of second order in Banach spaces

2018 ◽  
Vol 16 (1) ◽  
pp. 268-275
Author(s):  
Kamal N. Soltanov
Keyword(s):  
Differential Equation ◽  
Evolution Equation ◽  
Banach Spaces ◽  
Traffic Flow ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Nonlinear Hyperbolic Equation ◽  
Existence Of A Solution ◽  
Special Case

AbstractHere we study the existence of a solution and also the behavior of the existing solution of the abstract nonlinear differential equation of second order that, in particular, is the nonlinear hyperbolic equation with nonlinear main parts, and in the special case, is the equation of the type of equation of traffic flow.

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