Dipankar Kumar scite author profile

The present paper studies the unstable nonlinear Schrödinger equations, describing the time evolution of disturbances in marginally stable or unstable media. More precisely, the unstable nonlinear Schrödinger equation and its modified form are analytically solved using two efficient distinct techniques, known as the modified Kudraysov method and the sine-Gordon expansion approach. As a result, a wide range of new exact traveling wave solutions for the unstable nonlinear Schrödinger equation and its modified form are formally obtained.

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Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

Seadawy

2018

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New closed form soliton and other solutions of the Kundu–Eckhaus equation via the extended sinh-Gordon equation expansion method

Kumar

Manafian

Hawlader

et al. 2018

Optik

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New optical solitons of cubic-quartic nonlinear Schrödinger equation

Hosseini

Samadani

Kumar

et al. 2018

Optik

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New exact solutions for the time fractional coupled Boussinesq–Burger equation and approximate long water wave equation in shallow water

Khater

Kumar

2017

Journal of Ocean Engineering and Science

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Dynamics of two-mode Sawada-Kotera equation: Mathematical and graphical analysis of its dual-wave solutions

et al. 2020

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Dipankar Kumar

Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology

The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzéica type equations in nonlinear optics

New Exact Traveling Wave Solutions of the Unstable Nonlinear Schrödinger Equations

Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

New closed form soliton and other solutions of the Kundu–Eckhaus equation via the extended sinh-Gordon equation expansion method

New optical solitons of cubic-quartic nonlinear Schrödinger equation

New exact solutions for the time fractional coupled Boussinesq–Burger equation and approximate long water wave equation in shallow water

Dynamics of two-mode Sawada-Kotera equation: Mathematical and graphical analysis of its dual-wave solutions

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