Solitons and other solutions to nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity using several different techniques

The (1 + 2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity is studied using the factorization technique, bifurcation theory of dynamical system, and phase portraits analysis. From a dynamic point of view, the existence of smooth solitary wave, and kink and antikink waves is proved and all possible explicit parametric representations of these waves are presented.

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Study of modulation instability analysis and optical soliton solutions of higher-order dispersive nonlinear Schrödinger equation with dual-power law nonlinearity

Modern Physics Letters B ◽

10.1142/s0217984919503093 ◽

2019 ◽

Vol 33 (25) ◽

pp. 1950309

Author(s):

Naila Nasreen ◽

Aly R. Seadawy ◽

Dianchen Lu

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Power Law ◽

Schrodinger Equation ◽

Modulation Instability ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Mapping Technique ◽

Nonlinear Schrödinger ◽

Dual Power

In this paper, based on proposed Riccati mapping technique, we investigated the soliton solutions of fourth-order dispersive nonlinear Schrödinger equation with nonlinearity of dual-power law. The various types of solitons solutions involving some parameters are constructed. These soliton solutions can be useful for understanding the physical nature of the waves spread in the dispersive medium. Furthermore, the Modulation Instability (MI) is discussed by standard linear-stability analysis that shows all achieved results are exact and stable. The movements of some achieved results were presented graphically by giving suitable values to parameters that provide easy understanding to the physical phenomenon of this dynamical model. The obtained results show the simplicity and efficiency of the current used approach.

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Modulational Instability of the Higher-Order Nonlinear Schrödinger Equation with Fourth-Order Dispersion and Quintic Nonlinear Terms

Zeitschrift für Naturforschung A ◽

10.1515/zna-2006-5-603 ◽

2006 ◽

Vol 61 (5-6) ◽

pp. 225-234 ◽

Cited By ~ 6

Author(s):

Woo-Pyo Hong

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Modulational Instability ◽

Higher Order ◽

Nonlinear Schrodinger Equation ◽

Normal Dispersion ◽

Nonlinear Schrödinger ◽

Order Dispersion

The modulational instability of the higher-order nonlinear Schrödinger equation with fourth-order dispersion and quintic nonlinear terms, describing the propagation of extremely short pulses, is investigated. Several types of gains by modulational instability are shown to exist in both the anomalous and normal dispersion regimes depending on the sign and strength of the higher-order nonlinear terms. The evolution of the modulational instability in both the anomalous and normal dispersion regimes is numerically investigated and the effects of the higher-order dispersion and nonlinear terms on the formation and evolution of the solitons induced by modulational instability are studied. - PACS numbers: 42.65.Tg, 42.81Dp, 42.65Sf

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