Soliton solutions of multicomponent nonlinear Schrödinger equation

Nogami, Y.; Warke, C. S.

doi:10.1016/0375-9601(76)90782-9

Cited by 68 publications

(59 citation statements)

References 6 publications

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“…In particular, the theorem of Grillakis et al [15] guarantees the soliton instability provided the difference n(Λ) − p(U ) is odd. However, our results predict that the soliton instability always occurs for n(Λ) − p(U ) > 0, being associated with exactly n(Λ) − p(U ) non-negative real eigenvalues λ of the linear eigenvalue problem (4). Moreover, according to our result (iv), each new unstable eigenvalue λ appears via a bifurcation at the marginal stability curve where the determinant of the matrix U vanishes, i.e.…”

Section: Model and Basic Resultsmentioning

confidence: 50%

Stability criterion for multicomponent solitary waves

Pelinovsky

Kivshar

2000

Phys. Rev. E

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We obtain the most general matrix criterion for stability and instability of multi-component solitary waves considering a system of N incoherently coupled nonlinear Schrödinger equations. Soliton stability is studied as a constrained variational problem which is reduced to finite-dimensional linear algebra. We prove that unstable (all real and positive) eigenvalues of the linear stability problem for multi-component solitary waves are connected with negative eigenvalues of the Hessian matrix, the latter is constructed for the energetic surface of N −component spatially localized stationary solutions.

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Section: Model and Basic Resultsmentioning

confidence: 50%

Stability criterion for multicomponent solitary waves

Pelinovsky

Kivshar

2000

Phys. Rev. E

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“…Let us first look at the LO equation (25) which has the form of the multi-component non-linear Schrödinger (NLS) equation [17]. We notice that it does not contain γ at all, so that the same equation is valid independently of the bare fermion mass.…”

Section: Expansion Parameter Lo and Nlo Tdhf Equationsmentioning

confidence: 99%

Beyond integrability: Baryon-baryon backward scattering in the massive Gross-Neveu model

Thies

2017

Phys. Rev. D

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Due to integrability, baryon-baryon scattering in the massless Gross-Neveu model at large N features only forward elastic scattering. A bare mass term breaks integrability and is therefore expected to induce backward elastic scattering as well as inelastic reactions. We confirm these expectations by a study of baryon-baryon scattering in the massive Gross-Neveu model near the non-relativistic limit. This restriction enables us to solve the time-dependent Hartree-Fock equations with controlled approximations, using a combination of analytical methods from an effective field theory and the numerical solution of partial differential equations.

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“…As follows from the IST, it is possible to construct the full solution by adding the radiation modes to bright MSCs. On the other hand, solutions for bright MSCs, having a zero far-field asymptotic in the self-focusing medium (s = +1) can be found by solving a set of linear equations [18,19]:…”

Section: Explicit Solutions For Multi-soliton Complexes On a Bacmentioning

confidence: 99%