Non-existence of certain elliptic solutions of the Cubic-nonlinear Schr\"odinger Equation
Hans Werner Sch\"urmann, Valery Serov
TL;DR
This paper proves the non-existence of certain elliptic solutions for the cubic nonlinear Schrödinger equation in the generic case and characterizes solutions in the nongeneric case.
Contribution
It establishes non-existence results for a class of solutions and describes a two-parameter set of solutions in the nongeneric case.
Findings
Non-existence of certain elliptic solutions in the generic case.
Existence of a two-parameter set of solutions in the nongeneric case.
Solutions can be bounded or unbounded depending on constraints.
Abstract
For a certain class of solutions of the cubic nonlinear Sch\"odinger equation we prove non-existence in the generic case. In the nongeneric case we present a two-parameter set of solutions, bounded or unbounded, depending on corresponding constraints.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Partial Differential Equations · Nonlinear Differential Equations Analysis