Weak asymptotics method and the interaction of infinitely narrow \(\delta\)-solitons.
The authors consider a KdV-type equation of the form \[ u_t+(u^m)_x + \varepsilon^2u_{xxx}=0, \] where \(m\geq2\) is integer, \(\varepsilon\to+0\) is a small parameter. The interaction of solitons for the equation is studied. It is proposed some general procedure (the weak asymptotics method) for describing the interaction of nonlinear waves in both the integrable (\(m=2,3\)) and nonintegrable (\(m>3\)) cases. A suitable definition of the weak asymptotic solution is given in the paper.
scientific article; zbMATH DE number 1957315