Bifurcation of solitary and periodic waves of an extended cubic-quintic Schrödinger equation with nonlinear dispersion effects governing modulated waves in a bandpass inductor-capacitor network

2021 ◽  
Vol 152 ◽  
pp. 111397
Author(s):  
Guy Roger Deffo ◽  
Serge Bruno Yamgoué ◽  
François Beceau Pelap
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Periodic Waves ◽  
Nonlinear Dispersion ◽  
Dispersion Effects ◽  
Modulated Waves

ON NEW EXACT SPECIAL SOLUTIONS OF THEGNLS(m,n,p,q) EQUATIONS

2010 ◽  
Vol 24 (16) ◽  
pp. 1769-1783 ◽  
Author(s):  
MUSTAFA INÇ
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Dispersion ◽  
Nonlinear Schrödinger ◽  
Special Solutions ◽  
Generalized Nonlinear Schrödinger Equation

In this paper, we establish exact special solutions of the generalized nonlinear Schrödinger equation with nonlinear dispersion (called the GNLS (m,n,p,q) equation) by using a sn - cn method. Some new Jacobi elliptic, envelope compacton and solitary pattern solutions of GNLS (m,n,p,q) equations are obtained.

Nonlinear dispersion relation for nonlinear Schrödinger equation

1988 ◽  
Vol 39 (2) ◽  
pp. 297-302 ◽  
Author(s):  
J. C. Bhakta
Keyword(s):  
Dispersion Relation ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Instability Region ◽  
Nonlinear Dispersion ◽  
Nonlinear Schrödinger ◽  
Nonlinear Dispersion Relation ◽  
Cubic Nonlinear Schrödinger Equation

By using the average-Lagrangian method (average variational principle), a nonlinear dispersion relation has been derived for the cubic nonlinear Schrödinger equation. It is found that the size of the instability region in wavenumber space decreases with increasing field amplitude in comparison with the linear theory.

scholarly journals Rogue periodic waves of the focusing nonlinear Schrödinger equation

2018 ◽  
Vol 474 (2210) ◽  
pp. 20170814 ◽  
Author(s):  
Jinbing Chen ◽  
Dmitry E. Pelinovsky
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Elliptic Functions ◽  
Nonlinear Schrodinger Equation ◽  
Periodic Waves ◽  
Jacobian Elliptic Functions ◽  
Nonlinear Schrödinger

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn . Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov–Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine’s breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

scholarly journals Analytical Solutions to Generalized Nonlinear Schrödinger Equation by Adomian Decomposition Technique

2019 ◽  
pp. 1-11
Author(s):  
Villévo Adanhounme ◽  
Gaston Edah ◽  
Norbert M. Hounkonnou
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Adomian Decomposition Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Propagation ◽  
Initial Condition ◽  
Nonlinear Schrödinger ◽  
Dispersion Effects ◽  
Adomian Decomposition

We study the higher-order nonlinear Schrödinger equation which takes care of the second as well as third order dispersion effects, cubic and quintic self phase modulations, self steepening and nonlinear dispersion effects. Taking advantage of the initial condition, we transform theprevious equation into a nonlinear functional equation to which we apply a powerful analytical method called the Adomian decomposition method. We compute the Adomian’s polynomials of corresponding infinite series solution. Assuming that the initial condition and all its derivatives converge to zero sufficiently rapidly as the time approaches to infinity, we established the convergence of the previous series. The last part of the paper describes applications resulting from nonlinear propagation phenomena in optical fibers. Numerical simulations are developed and it is further shown that comparison with other results yields a good qualitative agreement. These results demonstrate the robustness of the proposed method.

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