1,289 Results Found

In this paper, we propose a reliable treatment for studying the two-wave (symbiotic) solitons of interactions in nonlinear quadratic media. We investigate the Schauder’s fixed point theorem for proving the existence theorem. Additionally, the u...

In this study, we consider a (2+1)-dimensional integrable Boussinesq equation, where the Hirota method of positive logarithmic transformation is used to convert it into a bilinear form. We proceeded by employing different test functions, through whic...

In this study, a dimensionally nonlinear evolution equation, which is the integrable shallow water wave-like equation, is investigated utilizing the Hirota bilinear approach. Lump solutions are achieved by its bilinear form and are essential solution...

A new two-mode version of the generalized Zakharov-Kuznetsov equation is derived using Korsunsky’s method. This dynamical model describes the propagation of two-wave solitons moving simultaneously in the same direction with mutual interaction t...

In this paper, we present new dynamical properties of the two-mode Caudrey–Dodd–Gibbon (TMCDG) equation. This equation describes the propagation of dual waves in the same direction with different phase velocities, dispersion parameters, a...

The forced Korteweg-de Vries equation is considered to investigate the impact of bottom configurations on the free surface waves in a two-dimensional channel flow. In the study of shallow water waves, the bottom topography plays a critical role, whic...

In this paper, the Hirota bilinear method, which is an important scheme, is used. The equation of the shallow water wave in oceanography and atmospheric science is extended to (3+1) dimensions, which is a well-known equation. A lot of classes of rati...

This paper explores some frame bundles and physical implications of Killing vector fields on the two-sphere ${\mathbb{S}}^2$, culminating in a novel application to Maxwell’s equations in free space. Initially, we investigate the Killing vector fields on ${\mathbb{S}}^2$ (...

In this article, we construct the exact dynamical wave solutions to the Date–Jimbo–Kashiwara–Miwa equation with conformable derivative by using an efficient and well-established approach, namely: the two-variable $\left(G’/G, \&n\right)$...

The asymptotic approach is suggested for the description of interacting surface and internal oceanic solitary waves. This approach allows one to describe stationary moving symmetric wave patterns consisting of two plane solitary waves of equal amplit...

We present and amplify some of our previous statements on non-canonical interrelations between the solutions to free Dirac equation (DE) and Klein–Gordon equation (KGE). We demonstrate that all the solutions to the DE (possessing point- or stri...

A technique for obtaining refined heuristic solutions for problems with electromagnetic wave diffraction by scatterers with non-ideal boundary conditions is proposed. Based on the method of fundamental components for the problem of TE-polarized wave...

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation,...

This paper presents the influence of the finite element mesh structure on the accuracy of the numerical solution of a two-dimensional linear kinematic wave equation. This equation was solved using a two-level scheme for time integration and a modifie...

We apply the Simple Equations Method (SEsM) for obtaining exact travelling-wave solutions of the extended fifth-order Korteweg-de Vries (KdV) equation. We present the solution of this equation as a composite function of two functions of two independe...

We consider a generalization of the modified Korteweg–de Vries–Burgers equation with a nonlinear source. Using the Painlevé test for partial differential equation with the Kruskal variable, we show that the corresponding Cauchy pro...

We extend two KdVSKR models to fractional KdVSKR models with the Caputo derivative. The KdVSKR equation in (2+1)-dimension, which is a recent extension of the KdVSKR equation in (1+1)-dimension, can model the soliton resonances in shallow water. Appl...

In this paper, two-dimensional Genocchi polynomials and the Ritz–Galerkin method were developed to investigate the Fractional Diffusion Wave Equation (FDWE) and the Fractional Klein–Gordon Equation (FKGE). A satisfier function that satisf...

In this work, we explore the nonlinear wave phenomena of the (3+1)-dimensional Boussinesq (II) equation, a significantly higher-dimensional model that describes dispersive wave propagation in fluid dynamics, plasma systems, and nonlinear optics. Usin...

An internal wave is a typical dynamic process. As an internal wave, an internal solitary wave usually occurs between two layers of fluids with different densities. Compared with general internal waves, internal solitary waves have large amplitudes, f...

Depressive symptomatology is associated with caregiver burden and poor health outcomes among dementia caregivers. Scholars called for a paradigm shift to focus on positive aspects of caregiving, in particular, meaning making during the caregiving jou...

Increasingly, manufacturing enterprises are compelled to pursue innovative solutions to environmental issues. Addressing such issues requires mindful leadership to support employees and organizations in maintaining awareness during complex situations...

Marital relationship quality significantly influences health outcomes, but validated measurement tools for South Asian populations remain limited. To validate scales measuring trust, commitment, and satisfaction as key components of marital relations...

Absolute distance determination in the open air with an uncertainty of a few tenths of a millimetre is increasingly required in many applications that involve high precision geodetic metrology. No matter the technique used to measure, the resulting d...

Within this work are analyzed third-order nonlinear optical properties with a potential influence on the dynamic mechanics exhibited by metal/carbon nanofluids. The nanofluids were integrated by multiwall carbon nanotubes decorated with Ag nanopartic...

Most studies of the localized edge (EM) and defect (DM) modes in cholesteric liquid crystals (CLC) are related to the localized modes in a collinear geometry, i.e., for the case of light propagation along the spiral axis. It is due to the fact that a...

This study focuses on investigating the modified Benjamin-Bona-Mahony equation that is used to model the long wave in nonlinear dispersive media of the optical illusion field. Two effective techniques, the variational direct method and He’s fre...

Gravitational waves are regarded as linear waves in the weak field approximation, which ignores the spacetime singularity. In this paper, we analyze singularities in exact gravitational wave solutions. We provide an exact general solution of the grav...

In this paper, we use a new, extended Jacobian elliptic function expansion method to explore the exact solutions of the (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov (aNNV) equation, which is a nonlinear physical model to describe...

Traveling wave solutions, including localized and periodic structures (e.g., solitary waves, cnoidal waves, and periodic waves), to a symmetry Korteweg–de Vries equation (KdV) with integer and rational power law nonlinearity are reported using...

We explore stochastic–fractional Drinfel’d–Sokolov–Wilson (SFDSW) equations for some wave solutions such as the cross-kink rational wave solution, periodic cross-rational wave solution and homoclinic breather wave solution. We...

The interaction of two simple delta shock waves for a pressureless gas dynamic system is considered. The result of the interaction is a delta shock wave with constant speed. This interaction is approximated by letting the perturbed parameter in the E...

In this article, we present the extended simple equations method (SEsM) for finding exact solutions to systems of fractional nonlinear partial differential equations (FNPDEs). The expansions made to the original SEsM algorithm are implemented in seve...

In this paper, a variable-coefficient Davey–Stewartson (vcDS) system is investigated for modeling the evolution of a two-dimensional wave-packet on water of finite depth in inhomogeneous media or nonuniform boundaries, which is where its novelt...

In the present study, two effective methods, the Exp-function method and He’s frequency formulation, are employed to investigate the dynamic behaviors of the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation, which is use...

We propose a new two-parameter family of hybrid traveling-standing (TS) water waves in infinite depth that evolve to a spatial translation of their initial condition at a later time. We use the square root of the energy as an amplitude parameter and...

A nonlinear $(3+1)$-dimensional nonlinear Geng equation that can be utilized to explain the dynamics of shallow-water waves in fluids is given special attention. Various wave solutions are produced with the aid of the Hirota bilinear and Cole–Hop...

In this study, we propose a generalized framework based on the Simple Equations Method (SEsM) for finding exact solutions to systems of fractional nonlinear partial differential equations (FNPDEs). The key developments over the original SEsM in the p...

The goal of this research is to utilize some ansatz forms of solutions to obtain novel forms of soliton solutions for the Benney–Luke equation. It is a mathematically valid approximation that describes the propagation of two-way water waves in...

We explore various analytical rational solutions with symbolic computation using the ansatz transformation functions. We gain a variety of rational solutions such as M-shaped rational solutions (MSRs), periodic cross-rationals (PCRs), multi-wave solu...

In this paper, we apply two different methods, namely, the $\frac{G^{\prime }}{G}$-expansion method and the $\frac{G^{\prime }}{G^2}$-expansion method to investigate the nonlinear time fractional Harry Dym equation in the Caputo sense and the symmetric regularized long wave equa...

The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions...

This research paper is about the new three wave, periodic wave and other analytical wave solutions of (2+1)-Dimensional Burgers equations by utilizing Hirota bilinear and extended sinh-Gordon equation expansion (EShGEE) schemes. Achieved solutions ar...

Transformations are much used to connect complicated nonlinear differential equations to simple equations with known exact solutions. Two examples of this are the Hopf–Cole transformation and the simple equations method. In this article, we fol...

This paper investigates the ion-acoustic wave structures in fluid ions for the Benjamin–Bona–Mahony–Peregrine–Burgers (BBMPB) equation. The various types of wave structures are extracted including the three-wave hypothesis, br...

In this paper, we study the symmetric travelling wave solutions of the b-family of the Novikov equation. We show that the b-family of the Novikov equation can provide symmetric travelling wave solutions, such as peakon, kink and smooth soliton soluti...

Shock wave therapy involves introducing an acoustic wave into the living organism, whose pro-healing effect promotes the decomposition of stones and calcareous deposits. To generate such a wave, devices converting electrical energy into shock wave en...

The second-order partial differential wave Equation (Cauchy’s first equation of motion), derived from Newton’s force equilibrium, describes a standing wave field consisting of two waves propagating in opposite directions, and is, therefor...

Nonlocal nonlinear Schrödinger equations are among the important models of nonlocal integrable systems. This paper aims to present a general formula for arbitrary-order breather solutions to multi-component nonlocal nonlinear Schrödinger eq...

This paper presents a novel analytical solution, which is developed for investigating three-dimensional wave-induced seabed responses for anisotropic permeability. The analytical solution is based on the assumption of the poroelastic and the $u-$...