Three-dimensional nonlinear Schrödinger equation for plasma waves

The three-dimensional evolution of packets of gravity waves is studied using a nonlinear Schrödinger equation (the Davey–Stewartson equation). It is shown that permanent wave groups of the elliptic en and dn functions and their common limiting solitary sech forms exist and propagate along directions making an angle less than ψc= tan−1(1/√2) = 35° with the underlying wave field, whilst, along directions making an angle greater than ψc, there exist permanent wave groups of elliptic sn and negative solitary tanh form. Furthermore, exact general solutions are given showing wave groups travelling along the two characteristic directions at ψcor − ψc. These latter solutions tend to form regions of large wave slope and are used to discuss the waves produced by a ship, in particular the nonlinear evolution of the leading edge of the pattern.

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Exact spatiotemporal soliton solutions to the generalized three-dimensional nonlinear Schrödinger equation in optical fiber communication

Advances in Difference Equations ◽

10.1186/s13662-015-0683-4 ◽

2015 ◽

Vol 2015 (1) ◽

Cited By ~ 2

Author(s):

Xiaoli Wang ◽

Jie Yang

Keyword(s):

Schrödinger Equation ◽

Optical Fiber ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Three Dimensional ◽

Soliton Solutions ◽

Optical Fiber Communication ◽

Nonlinear Schrodinger Equation ◽

Fiber Communication ◽

Nonlinear Schrödinger

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Solitary wave solutions of chiral nonlinear Schrödinger equations

Modern Physics Letters B ◽

10.1142/s0217984921504728 ◽

2021 ◽

pp. 2150472

Author(s):

Handenur Esen ◽

Neslihan Ozdemir ◽

Aydin Secer ◽

Mustafa Bayram ◽

Tukur Abdulkadir Sulaiman ◽

...

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Three Dimensional ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Physical Models ◽

Edge States ◽

Fractional Quantum Hall ◽

Nonlinear Schrödinger

This paper presents the (1+1)-dimensional chiral nonlinear Schrödinger equation (1DCNLSE) and (2+1)-dimensional chiral nonlinear Schrödinger equation (2DCNLSE) that define the edge states of the fractional quantum hall effect. In this paper, we implement the Riccati–Bernoulli sub-ODE method in reporting the solutions of these two nonlinear physical models. As a result of this, some singular periodic waves, dark and singular optical soliton solutions are generated for these models. Some of the acquired solutions are illustrated by three-dimensional (3D) and two-dimensional (2D) graphs utilizing suitable values of the parameters with the help of the MAPLE software to demonstrate the importance in the real-world of the presented equations.

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Curvilinear coordinate lattice Boltzmann simulation for necklace-ring beams in the nonlinear Schrödinger equation

International Journal of Modern Physics C ◽

10.1142/s0129183120501363 ◽

2020 ◽

Vol 31 (10) ◽

pp. 2050136

Author(s):

Boyu Wang ◽

Jianying Zhang ◽

Guangwu Yan

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Lattice Boltzmann ◽

Schrodinger Equation ◽

Dimensional Space ◽

Time Derivative ◽

Three Dimensional ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Curvilinear Coordinate

Necklace-ring solitons have gained much attention due to their potential applications in optics and other scientific areas. In this paper, the numerical investigation of the nonlinear Schrödinger equation by using the curvilinear coordinate lattice Boltzmann method is proposed to study necklace-ring solitons. Different from those used in the general curvilinear coordinate lattice Boltzmann models, the lattices used in this work are uniform in two- and three-dimensional space. Furthermore, the model contains spatial evolution rather than time evolution to avoid the complexity of dealing with higher-order time derivative terms as well as to maintain the simplicity of the algorithm. Numerical experiments reproduce the evolution of two- and three-dimensional necklace-ring solitons. The truncation error analysis indicates that our model is equivalent to the Crank–Nicolson difference scheme.

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