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Influence of uncertain coriolis parameter on wave solution of Korteweg-de Vries equation
This article examines the approximate solution of the Geophysical Korteweg-de Vries (GKdV) equation in a fuzzy environment. The Adomian decomposition...
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Hetero-Bäcklund Transformation, Bilinear Forms and N Solitons for a Generalized Three-Coupled Korteweg-de Vries System
Korteweg-de Vries-type models attract people’s attention during the studies on the cosmic plasmas, planetary oceans and atmospheres. In this paper,...
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The geophysical KdV equation: its solitons, complexiton, and conservation laws
The main goal of the current paper is to analyze the impact of the Coriolis parameter on nonlinear waves by studying the geophysical KdV equation....
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On the Comparison of Two Meshless Finite Difference Methods for Solving Shallow Water Equations
In this article, we present a numerical analysis of the Korteweg-de Vries (KdV) and Regularized Long Wave (RLW) equations using a finite difference...
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Dynamics of Rossby solitary waves with time-dependent mean flow via Euler eigenvalue model
The investigation on the fluctuations of nonlinear Rossby waves is of great importance for the understanding of atmospheric or oceanic motions. The...
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Bilinear Form, Bilinear Bäcklund Transformations, Breather and Periodic-Wave Solutions for a (2+1)-Dimensional Shallow Water Equation with the Time-Dependent Coefficients
Shallow water waves are seen in geophysical fluid dynamics, oceanography, coastal engineering and atmospheric science. In this paper, to describe the...
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On the Geophysical Green-Naghdi System
In this paper, a modified Green-Naghdi system with the effect of the Coriolis force is derived, which is a model in the equatorial oceanography to...
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Modulation Analysis of the Stochastic Camassa–Holm Equation with Pure Jump Noise
We study the stochastic Camassa–Holm equation with pure jump noise. We prove that if the initial condition of the solution is a solitary wave...
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Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma
The one-dimensional nonlinear dynamical wave interactions in a system of quasineutral two-fluid plasma in a constant magnetic field are investigated....
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A spectral method based on Bernstein orthonormal basis functions for solving an inverse Roseneau equation
In this work, we study an inverse problem with unknown boundary conditions in the one-dimensional Rosenau equation. It is assumed that we have extra...
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Structure-Preserving Reduced- Order Modeling of Non-Traditional Shallow Water Equation
An energy- preserving reduced -order model (ROM) is developed for the non-traditional shallow water equation (NTSWE) with full Coriolis force. The...
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A mixed approximate method to simulate generalized Hirota–Satsuma coupled KdV equations
A mixed approximate method is proposed to simulate the generalized Hirota–Satsuma coupled Korteweg–de Vries equations. The equations are represented...
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Benjamin–Ono and Intermediate Long Wave Equations: Modeling, IST and PDE
This chapter focuses on two asymptotic models for internalwaves, the Benjamin–Ono (BO) and Intermediate LongWave (ILW) equations, which are...
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Approximate Analytical Solutions of Generalized Zakharov–Kuznetsov and Generalized Modified Zakharov–Kuznetsov Equations
This paper investigates the generalized Zakharov–Kuznetsov (GZK) equation and generalized modified Zakharov–Kuznetsov equation in the presence of...
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Dispersion in Shallow Moment Equations
Shallow moment models are extensions of the hyperbolic shallow water equations. They admit variations in the vertical profile of the horizontal...
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Combined effects of topography and bottom friction on shoaling internal solitary waves in the South China Sea
A numerical study to a generalized Korteweg-de Vries (KdV) equation is adopted to model the propagation and disintegration of large-amplitude...
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Double-periodic soliton solutions for the new (2 + 1)-dimensional KdV equation in fluid flows and plasma physics
Based on the extended homoclinic test technique, we introduce an ansätz functions to construct double periodic-soliton solutions of new...
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Kadomtsev–Petviashvili and Related Equations
This chapter aims to survey the known results on the Kadomtsevs–Petviashvili equations and their variants from the point of viewof modeling, PDEs and...
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Continuous Data Assimilation with Blurred-in-Time Measurements of the Surface Quasi-Geostrophic Equation
An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. The authors consider...