Nonexistence of travelling wave solutions to nonelliptic nonlinear schrödinger equations
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By deriving Pohojaev-type identities we prove that nonelliptic nonlinear Schrödinger equations do not admit localized travelling wave solutions. Similary, we prove that the Davey-Stewartson hyperbolic-elliptic systems do not support travelling wave solutions except for a specific range of the parameters that comprises the DS II focusing case (where the existence of lumps is well known).
KeywordsCauchy Problem Wave Solution Travel Wave Solution Positive Radial Solution Inverse Scattering Transform
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