Exact Kink Solitons in the Presence of Diffusion, Dispersion, and Polynomial Nonlinearity

Details Exact Kink Solitons in the Presence of Diffusion, Dispersion, and Polynomial Nonlinearity Exact Kink Solitons in the Presence of Diffusion, Dispersion, and Polynomial Nonlinearity

1998-05-19

arxiv.org/abs/solv-int/9805008v1

Physics

Condensed Matter

11 pages, Latex

Scientific paper

10.1016/S0375-9601(99)00067-5

We describe exact kink soliton solutions to nonlinear partial differential equations in the generic form u_{t} + P(u) u_{x} + \nu u_{xx} + \delta u_{xxx} = A(u), with polynomial functions P(u) and A(u) of u=u(x,t), whose generality allows the identification with a number of relevant equations in physics. We emphasize the study of chirality of the solutions, and its relation with diffusion, dispersion, and nonlinear effects, as well as its dependence on the parity of the polynomials $P(u)$ and $A(u)$ with respect to the discrete symmetry $u\to-u$. We analyze two types of kink soliton solutions, which are also solutions to 1+1 dimensional phi^{4} and phi^{6} field theories.

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