Can a Non-Linear Differential Equation Have a Soliton Solution?

[caduceus]

I have a non-linear differential equation and I wonder whether it has a soliton solution or not. How can I approach to the problem?

So far I have never dealt with non-linear differential equations, hence, any suggestion is appreciated.

 

[Sourabh N]

I don't know of any general criteria for a soliton solution. One criteria for one kind of solitons is, the solution approaches different limits as the independent variable goes to + and - infinities (with additional constraints)

Maybe it'll be easier to help if you can write the non-linear equation you have.

 

[arildno]

IF there is a soliton solution to your diff.eq (let's say it concerns water waves), and that this soliton is to retain its shape&propagation velocity, then, in the 2-D case, your free surface should be writable as a function f(x-c*t), (rather than the general case f(x,t)).

This is then a necessary criterion for the existence of a soliton of this type; by studying your diff.eq further, you will find out if such a solution in fact exists.