Anti-periodic traveling wave solutions to a forced two-dimensional generalized Korteweg-de Vries equation (Q2367815)

Travelling-wave solutions to the generalized Kadomtsev-Petviashvili equation, \[ \biggl(u_ t+\bigl(f(u)\bigr)_ x+\alpha u_{xxx}\biggr)_ x+\beta u_{yy}+g=0, \] are considered, where \(f(u)\) is a sufficiently general nonlinear function, \(g\) is a free term of the inhomogeneous equation, \(\alpha\) and \(\beta\) are real constants. The travelling-wave solution is sought for in the form \(u=u(ax+by-\omega t)\), so that the free term \(g\) is assumed to be a function of the same argument. Using the fixed-point theorem, the authors prove existence and uniqueness of a solution to this problem satisfying the antiperiodicity condition, \(u(x+L)=-u(x)\), with some period \(L\).