Dark Soliton in Long and Short Wave Resonant Interaction

Sakai, Kiyoshi; Noguchi, Akira

doi:10.1143/jpsj.49.2009

Cited by 1 publication

(3 citation statements)

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“…We shall adopt the Hirota approach, as the algebra is slightly simpler. The appropriate expansion is (p real, Ω complex) (2) ), (ρ 0 = constant = amplitude in the far field)…”

Section: The Breather Solution For the Long Wave-short Wave Resonancementioning

confidence: 99%

“…The major distinction from the corresponding case of the NLS equation is the presence of a complex frequency Ω. ζ (1) , ζ (2) are arbitrary phase factors. Using the bilinear equations (3), the parameters, a 1 , a 2 are given by…”

Section: The Breather Solution For the Long Wave-short Wave Resonancementioning

confidence: 99%

“…To obtain a rogue wave mode, we perform a long wave limit expansion similar to that done in Section 2. On choosing exp(ζ (1) ) = exp(ζ (2) ) = -1, we obtain rogue wave modes where the short wave component is…”

Section: The Breather Solution For the Long Wave-short Wave Resonancementioning

confidence: 99%

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Rogue Wave Modes for the Long Wave–Short Wave Resonance Model

et al. 2013

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The long wave-short wave resonance model arises physically when the phase velocity of a long wave matches the group velocity of a short wave. It is a 2 system of nonlinear evolution equations solvable by the Hirota bilinear method and also possesses a Lax pair formulation. 'Rogue wave' modes, algebraically localized entities in both space and time, are constructed from the breathers by a singular limit involving a 'coalescence' of wavenumbers in the long wave regime. In contrast with the extensively studied nonlinear Schrödinger case, the frequency of the breather cannot be real and must satisfy a cubic equation with complex coefficients. The same limiting procedure applied to the finite wavenumber regime will yield mixed exponential-algebraic solitary waves, similar to the classical 'double pole' solutions of other evolution systems.

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“…We shall adopt the Hirota approach, as the algebra is slightly simpler. The appropriate expansion is (p real, Ω complex) (2) ), (ρ 0 = constant = amplitude in the far field)…”

Section: The Breather Solution For the Long Wave-short Wave Resonancementioning

confidence: 99%

Section: The Breather Solution For the Long Wave-short Wave Resonancementioning

confidence: 99%