scholarly journals New analytical solitary and periodic wave solutions for generalized variable-coefficients modified KdV equation with external-force term presenting atmospheric blocking in oceans

2021 ◽  
Author(s):  
Rehab M. El-Shiekh ◽  
Mahmoud Gaballah
Keyword(s):  
External Force ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Variable Coefficients ◽  
Force Term ◽  
Atmospheric Blocking ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Modified Kdv Equation

Study of the New Solitory Wave Solutions and Periodic Wave Solutions of a Two-Dimensional Modified KdV Equation

2013 ◽  
Vol 432 ◽  
pp. 122-126
Author(s):  
Mei Ling Gu ◽  
Zhi Hua Zhu ◽  
Song Hua Ma
Keyword(s):  
Kdv Equation ◽  
Periodic Wave ◽  
Mkdv Equation ◽  
Separation Method ◽  
Two Dimensional ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Modified Kdv Equation ◽  
Variable Separation Method

With the help of the Riccati mapping approach and the variable separation method, some new solitory wave solutions and periodic wave solutions of the two-dimensional modified KdV(MKdV) equation are derived.

Lump-type solutions, interaction solutions and periodic wave solutions of a (3+1)-dimensional Korteweg–de Vries equation

2019 ◽  
Vol 33 (27) ◽  
pp. 1950319 ◽  
Author(s):  
Hongfei Tian ◽  
Jinting Ha ◽  
Huiqun Zhang
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Interaction Solutions ◽  
Dynamical Behaviors ◽  
Wave Solutions ◽  
Hirota Bilinear Form ◽  
De Vries ◽  
Hirota Bilinear

Based on the Hirota bilinear form, lump-type solutions, interaction solutions and periodic wave solutions of a (3[Formula: see text]+[Formula: see text]1)-dimensional Korteweg–de Vries (KdV) equation are obtained. The interaction between a lump-type soliton and a stripe soliton including two phenomena: fission and fusion, are illustrated. The dynamical behaviors are shown more intuitively by graphics.

EXACT SOLITON SOLUTIONS AND QUASI-PERIODIC WAVE SOLUTIONS TO THE FORCED VARIABLE-COEFFICIENT KdV EQUATION

2012 ◽  
Vol 26 (19) ◽  
pp. 1250072 ◽  
Author(s):  
YI ZHANG ◽  
ZHILONG CHENG
Keyword(s):  
Variable Coefficient ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Time Dependent ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Hirota Bilinear ◽  
Exact Soliton Solutions

In this paper, the time-dependent variable-coefficient KdV equation with a forcing term is considered. Based on the Hirota bilinear method, the bilinear form of this equation is obtained, and the multi-soliton solutions are studied. Then the periodic wave solutions are obtained by using Riemann theta function, and it is also shown that classical soliton solutions can be reduced from the periodic wave solutions.

scholarly journals Numerical calculation of N -periodic wave solutions to coupled KdV–Toda-type equations

2021 ◽  
Vol 477 (2245) ◽  
pp. 20200752
Author(s):  
Yingnan Zhang ◽  
Xingbiao Hu ◽  
Jianqing Sun
Keyword(s):  
Toda Lattice ◽  
Kdv Equation ◽  
Direct Method ◽  
Periodic Wave ◽  
Periodic Waves ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Numerical Process ◽  
Relativistic Toda Lattice ◽  
Ito Equation

In this paper, we study the N -periodic wave solutions of coupled Korteweg–de Vries (KdV)–Toda-type equations. We present a numerical process to calculate the N -periodic waves based on the direct method of calculating periodic wave solutions proposed by Akira Nakamura. Particularly, in the case of N  = 3, we give some detailed examples to show the N -periodic wave solutions to the coupled Ramani equation, the Hirota–Satsuma coupled KdV equation, the coupled Ito equation, the Blaszak–Marciniak lattice, the semi-discrete KdV equation, the Leznov lattice and a relativistic Toda lattice.

scholarly journals Exact Peakon, Compacton, Solitary Wave, and Periodic Wave Solutions for a Generalized KdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-19
Author(s):  
Qing Meng ◽  
Bin He
Keyword(s):  
Dynamical System ◽  
Numerical Simulation ◽  
Solitary Wave ◽  
Planar Graphs ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Generalized Kdv Equation ◽  
Wave Solutions ◽  
Periodic Cusp Waves

We employ the approaches of both dynamical system and numerical simulation to investigate a generalized KdV equation, which is presented by Yin (2012). Some peakon, compacton, solitary wave, smooth periodic wave, and periodic cusp wave solutions are obtained, and the planar graphs of the compactons and the periodic cusp waves are simulated.

Chirped Wave Solutions of a Generalized (3+1)-Dimensional Nonlinear Schr¨odinger Equation

2011 ◽  
Vol 66 (6-7) ◽  
pp. 392-400 ◽  
Author(s):  
Xian-Jing Lai ◽  
Xiao-Ou Cai
Keyword(s):  
Dispersion Coefficient ◽  
Periodic Wave ◽  
Variable Coefficients ◽  
Nonlinearity Coefficient ◽  
Nonlinear Gain ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Self Similar ◽  
Linear And Nonlinear ◽  
Gain Loss

The exact chirped soliton-like and quasi-periodic wave solutions of the (3+1)-dimensional generalized nonlinear Schrödinger equation including linear and nonlinear gain (loss) with variable coefficients are obtained detailedly in this paper. The form and the behaviour of solutions are strongly affected by the modulation of both the dispersion coefficient and the nonlinearity coefficient. In addition, self-similar soliton-like waves precisely piloted from our obtained solutions by tailoring the dispersion and linear gain (loss)

On One- and Two-Periodic Wave Solutions of the Ninth-Order KdV Equation

2018 ◽  
Vol 103 (5-6) ◽  
pp. 943-951
Author(s):  
J. Pang ◽  
L. C. He ◽  
Z. L. Zhao
Keyword(s):  
Kdv Equation ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions

Obliquely propagating ion-acoustic nonlinear periodic waves in a magnetized plasma with two electron species

1994 ◽  
Vol 51 (3) ◽  
pp. 355-370 ◽  
Author(s):  
L. L. Yadav ◽  
R. S. Tiwari ◽  
S. R. Sharma
Keyword(s):  
Kdv Equation ◽  
Periodic Wave ◽  
Magnetized Plasma ◽  
Periodic Waves ◽  
Cnoidal Wave ◽  
Ion Temperature ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Ion Acoustic ◽  
De Vries

Obliquely propagating ion-acoustic nonlinear periodic waves in a magnetized plasma consisting of warm adiabatic ions and two Maxwellian electron species are studied. Using the reductive perturbation method, the Korteweg–de Vries (KdV) equation is derived and its cnoidal wave solution is discussed. It is found that as the amplitude of the cnoidal wave increases, so does its frequency. The effects of variations in the density and temperature ratios of the two electron species, the ion temperature, the angle of obliqueness and the magnetization on the characteristics of the cnoidal wave are discussed in detail. When the coefficient of the nonlinear term of the KdV equation, a1, vanishes, the modified Korteweg–de Vries equation is derived, and its periodic-wave solutions are discussed in detail. In the limiting case these periodic-wave solutions reduce to soliton or double-layer solutions.

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