Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. II: Complex analytic behavior and convergence to non-analytic solutions. (English) Zbl 0959.35157

Li, Y. A.; Olver, P. J.

Discrete Contin. Dyn. Syst. 4, No. 1, 159-191 (1998).

Part I appeared in [ibid. 3, No. 3, 419-432 (1997; Zbl 0949.35118)].
Summary: We prove that the solitary wave solutions of the integrable wave equation \[ u_t+\nu u_{xxt}=\alpha u_x+\beta u_{xxx}+\tfrac 3\nu uu_x+uu_{xxx}+2u_xu_{xx} \] investigated in part I are extended as analytic functions in the complex plane, except for at most countably many branch points and branch lines. We describe in detail how the limiting behavior of the complex singularities allows the creation of non-analytic solutions with corners and/or compact support.

MSC:

35Q58	Other completely integrable PDE (MSC2000)
37K40	Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
76B25	Solitary waves for incompressible inviscid fluids

Keywords:

solitary wave solutions; limiting behavior; non-analytic solutions

Citations:

Zbl 0949.35118