2 research outputs found
Exact Kink Solitons in the Presence of Diffusion, Dispersion, and Polynomial Nonlinearity
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 and with respect to the discrete
symmetry . We analyze two types of kink soliton solutions, which are
also solutions to 1+1 dimensional phi^{4} and phi^{6} field theories.Comment: 11 pages, Late
Chiral Solitons in Generalized Korteweg-de Vries Equations
Generalizations of the Korteweg-de Vries equation are considered, and some
explicit solutions are presented. There are situations where solutions engender
the interesting property of being chiral, that is, of having velocity
determined in terms of the parameters that define the generalized equation,
with a definite sign.Comment: 9 pages, latex, no figures. References added, typos correcte