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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
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
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