Approximate analytical solutions of fractional nonlinear Schrodinger equations using multistep modified reduced differential transform method

2019 ◽  
Author(s):  
Che Haziqah Che Hussin ◽  
Ahmad Izani Md Ismail ◽  
Adem Kilicman ◽  
Amirah Azmi
Keyword(s):  
Analytical Solutions ◽  
Differential Transform Method ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Transform Method ◽  
Nonlinear Schrödinger ◽  
Approximate Analytical Solutions ◽  
Nonlinear Schrodinger Equations ◽  
Differential Transform ◽  
Reduced Differential Transform Method

scholarly journals Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Zhoujin Cui ◽  
Zisen Mao ◽  
Sujuan Yang ◽  
Pinneng Yu
Keyword(s):  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Time Derivative ◽  
Differential Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Differential Transform ◽  
Reduced Differential Transform Method

The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The two different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance.

ANALYTICAL SOLUTIONS OF COUPLED NONLINEAR SCHRODINGER EQUATIONS FOR TWO NON LINEARLY INTERACTING STOKES WAVE TRAINS OVER INFINITE DEPTH

2021 ◽  
Vol 10 (3) ◽  
pp. 1137-1144
Author(s):  
S. Manna ◽  
A.K. Dhar
Keyword(s):  
Analytical Solutions ◽  
Nonlinear Schrödinger Equations ◽  
Stokes Wave ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Wave Trains ◽  
Coupled Nonlinear Schrodinger Equations

An attempt to find the exact analytical solutions of the two coupled nonlinear Schrodinger equations of 3rd order occurring from the oblique interaction of two capillary gravity wave trains in the case of crossing sea states in deep water is the main premise of the present paper. The solutions obtained here are due to the nonlinear interaction of two Stokes wave trains in one spatial dimension. Graphs have been plotted to investigate the influence of capillarity on the amplitudes of such wave trains. From 3D figures it has been observed that the capillarity has diminishing influence on the amplitudes of the either wave packet.

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