The bright<i>N</i>-soliton solution of a multi-component modified nonlinear Schrödinger equation

Matsuno, Yoshimasa

doi:10.1088/1751-8113/44/49/495202

Cited by 20 publications

(26 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…With the direct method, the bright N-soliton solution of (45) has been obtained in the form of compact determinantal expressions [22]. Our Darboux transformation method in the present paper can be easily generalized to m-component (45), then the bright vector N-soliton solution of (45) can be also derived in terms of the determinant representation.…”

Section: Discussionmentioning

confidence: 95%

Darboux Transformation and N-Soliton Solution for the Coupled Modified Nonlinear Schrödinger Equations

Zhang

2012

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

The pulse propagation in the picosecond or femtosecond regime of birefringent optical fibers is governed by the coupled mixed derivative nonlinear Schrödinger (CMDNLS) equations. A new type of Lax pair associated with such coupled equations is derived from the Wadati-Konno-Ichikawa spectral problem. The Darboux transformation method is applied to this integrable model, and the N-times iteration formula of the Darboux transformation is presented in terms of the compact determinant representation. Starting from the zero potential, the bright vector N-soliton solution of CMDNLS equations is expressed as a compact determinant by N complex eigenvalues and N linearly independent eigenfunctions. The collision mechanisms in two components shows that bright vector solitons can exhibit the standard elastic and inelastic collisions. Such energy-exchange collision behaviours have potential applications in the construction of logical gates, the design of fiber directional couplers, and quantum information processors.

show abstract

Section: Discussionmentioning

confidence: 95%

Darboux Transformation and N-Soliton Solution for the Coupled Modified Nonlinear Schrödinger Equations

Zhang

2012

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

show abstract

“…We consider the system of PDEs (1.1) subjected to the plane-wave boundary conditions (1.2). As in the case of zero boundary conditions considered in [13], we first apply the following gauge transformation…”

Section: Gauge Transformationmentioning

confidence: 99%

“…Here, p j and ζ j0 (j = 1, 2, ..., N) are arbitrary complex parameters characterizing the amplitude and phase of the solitons, respectively, and the N constraints are imposed on the parameters p j [13], the real part of p j is related to its imaginary part by (3.16). In the general n-component system, one needs to solve the algebraic equation of order n for (Re p j ) 2 .…”

Section: The Dark N-soliton Solutionmentioning

confidence: 99%

“…The proof will be performed by employing lemmas 3.1-3.4 and some basic formulas for determinants. In particular, Jacobi's identity (2.4) plays the central role, as in the case of the proof of the bright N-soliton solution of the modified NLS system (1.1) [13].…”

Section: Proof Of Theorem 31mentioning

confidence: 99%

“…The coefficients σ s = ±1 (s = 1, 2, ..., n) specify the sign of the nonlinearity. For the multi-component NLS system for which γ = 0, we can deal with the three types of cubic nonlinearities, i.e., focusing (σ s = 1, s = 1, 2, ..., n), defocusing (σ s = −1, s = 1, 2, ..., n) and mixed focusing-defocusing (σ s = 1, s = 1, 2, ..., m; σ s = −1, s = m + 1, m + 2, ..., n) nonlinearities with µ > 0, where m is an arbitrary positive integer such that 1 ≤ m < n. The special systems reduced from (1.1) have been summarized in a previous paper [13]. The system (1.1) has been shown to be completely integrable [14] and hence the exact methods mentioned above can be applied to it to obtain various types of soliton solutions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The multi-component modified nonlinear Schrödinger system with nonzero boundary conditions

Matsuno

2019

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

In a previous paper (Matsuno 2011 J. Phys. A: Math. Theore. 44 495202), we have presented a determinantal expression of the bright N-soliton solution for a multi-component modified nonlinear Schrödinger (NLS) system with zero boundary conditions. The present paper provides the dark N-soliton solution for the same system of equations with planewave boundary conditions, as well as the bright-dark N-soliton solution with mixed zero and plane-wave boundary conditions. The proof of the N-soliton solutions is performed by means of an elementary theory of determinants in which Jacobi's identity plays the central role. The N-soliton formulas obtained here include as special cases the existing soliton solutions of the NLS and derivative NLS equations and their integrable multicomponent analogs. The new features of soliton solutions are discussed. In particular, it is shown that the N constraints must be imposed on the amplitude parameters of solitons in constructing the dark N-soliton solution with plane-wave boundary conditions. This makes it difficult to analyze the solutions as the number of components increases. For mixed type boundary conditions, the structure of soliton solutions is found to be more explicit than that of dark soliton solutions since no constraints are imposed on the soliton parameters. Last, we comment on an integrable multi-component system associated with the first negative flow of the multi-component derivative NLS hierarchy.

show abstract

Conservation laws, modulation instability, and mixed semi‐rational solutions for a three‐component modified nonlinear Schrödinger equation

Xu,

Qiao

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

The brightN-soliton solution of a multi-component modified nonlinear Schrödinger equation

Cited by 20 publications

References 15 publications

Darboux Transformation and N-Soliton Solution for the Coupled Modified Nonlinear Schrödinger Equations

Darboux Transformation and N-Soliton Solution for the Coupled Modified Nonlinear Schrödinger Equations

The multi-component modified nonlinear Schrödinger system with nonzero boundary conditions

Conservation laws, modulation instability, and mixed semi‐rational solutions for a three‐component modified nonlinear Schrödinger equation

Contact Info

Product

Resources

About