scholarly journals Combined ZK-mZK equation for Rossby solitary waves with complete Coriolis force and its conservation laws as well as exact solutions

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Bao Jun Zhao ◽  
Ru Yun Wang ◽  
Wen Jin Sun ◽  
Hong Wei Yang
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Coriolis Force ◽  
Solitary Waves ◽  
Rossby Solitary Waves ◽  
Complete Coriolis Force

Structure of equatorial envelope Rossby solitary waves with complete Coriolis force and the external source

2018 ◽  
Vol 111 ◽  
pp. 68-74 ◽  
Author(s):  
Xiao-Jun Yin ◽  
Lian-Gui Yang ◽  
Quan-Sheng Liu ◽  
Jin-Mei Su ◽  
Guo-rong Wu
Keyword(s):  
Coriolis Force ◽  
Solitary Waves ◽  
External Source ◽  
Rossby Solitary Waves ◽  
Complete Coriolis Force

Conservation Laws of Space-Time Fractional mZK Equation for Rossby Solitary Waves with Complete Coriolis Force

2019 ◽  
Vol 20 (1) ◽  
pp. 17-32 ◽  
Author(s):  
Hong Wei Yang ◽  
Min Guo ◽  
Hailun He
Keyword(s):  
Coriolis Force ◽  
Solitary Waves ◽  
Inverse Method ◽  
Space Time ◽  
Atmospheric Physics ◽  
Similarity Reduction ◽  
Integer Order ◽  
Rossby Solitary Waves ◽  
New Research ◽  
Complete Coriolis Force

AbstractThe study of Rossby solitary waves are of great significance in physical oceanography, atmospheric physics, water conservancy project, military and communications engineering, etc. All the time, in the study of Rossby solitary waves, people have been focusing on integer order models. Recently, fractional calculus has become a new research hotspot, and it has opened a new door to research atmospheric and ocean. Thus, the fractional order model has the potential value in the study of Rossby solitary waves. In the present paper, according to the quasi-geostrophic potential vorticity equation with the complete Coriolis force, we get a new integer order mZK equation. Using the semi-inverse method and the fractional variational principle, the space-time fractional mZK(STFmZK) equation is obtained. To better understand the property of Rossby solitary waves, we study Lie symmetry analysis, nonlinear self-adjointness, similarity reduction by applying the STFmZK equation. In the end, the conservation and Caputo fractional derivative are discussed, respectively.

scholarly journals Conservation laws and exact solutions for the generalized Ostrovsky equation using symmetry analysis

2021 ◽  
Author(s):  
Sol Sáez
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Solitary Waves ◽  
Symmetry Analysis ◽  
Partial Differential ◽  
Wide Range ◽  
Depth Study ◽  
Ostrovsky Equation

In this work we consider a generalized Ostrovsky equation depending on two arbitrary functions and we make an in-depth study of this equation. We obtain the Lie symmetries which are admitted by this equation and some exact solutions as a periodic or solitary waves, obtained through ordinary and partial differential equations. Also, by means of the concept of multiplier, we obtain a wide range of conservation laws which preserve properties of the generalized Ostrovsky equation.

scholarly journals Benjamin-Ono-Burgers-MKdV Equation for Algebraic Rossby Solitary Waves in Stratified Fluids and Conservation Laws

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hongwei Yang ◽  
Shanshan Jin ◽  
Baoshu Yin
Keyword(s):  
Conservation Laws ◽  
Solitary Waves ◽  
Rossby Waves ◽  
Multiple Scale ◽  
Mkdv Equation ◽  
Center Of Gravity ◽  
Stratified Fluids ◽  
Scale Method ◽  
Small Dissipation ◽  
Rossby Solitary Waves

In the paper, by using multiple-scale method, the Benjamin-Ono-Burgers-MKdV (BO-B-MKdV) equation is obtained which governs algebraic Rossby solitary waves in stratified fluids. This equation is first derived for Rossby waves. By analysis and calculation, some conservation laws are derived from the BO-B-MKdV equation without dissipation. The results show that the mass, momentum, energy, and velocity of the center of gravity of algebraic Rossby waves are conserved and the presence of a small dissipation destroys these conservations.

A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws

2021 ◽  
Vol 143 ◽  
pp. 110486
Author(s):  
Nisa Çelik ◽  
Aly R. Seadawy ◽  
Yeşim Sağlam Özkan ◽  
Emrullah Yaşar
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Solitary Waves ◽  
Nonlinear Elastic

scholarly journals Exact Solutions and Conservation Laws of a (2+1)-Dimensional Nonlinear KP-BBM Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Khadijo Rashid Adem ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Solitary Waves ◽  
Lie Group ◽  
Group Analysis ◽  
Equation Method ◽  
Two Dimensional ◽  
Lie Group Analysis ◽  
Simplest Equation Method ◽  
Bbm Equation

In this paper, we study the two-dimensional nonlinear Kadomtsov-Petviashivilli-Benjamin-Bona-Mahony (KP-BBM) equation. This equation is the Benjamin-Bona-Mahony equation formulated in the KP sense. We first obtain exact solutions of this equation using the Lie group analysis and the simplest equation method. The solutions obtained are solitary waves. In addition, the conservation laws for the KP-BBM equation are constructed by using the multiplier method.

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

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