The Improved Generalized tanh-coth Method Applied to Sixth-Order Solitary Wave Equation by M. Torvattanabun, J. Simmapim, D. Saennuad, T. Somaumchan

“…This method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. The new exact solutions consisted of trigonometric functions solutions, hyperbolic functions solutions, exponential functions solutions, and rational functions solutions. …”
Get full text

The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions by Shoukry Ibrahim Atia El-Ganaini

“…The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1)-dimensional hyperbolic nonlinear Schrodinger (HNLS) equation, the generalized nonlinear Schrodinger (GNLS) equation with a source, and the higher-order nonlinear Schrodinger equation in nonlinear optical fibers. …”
Get full text

Global Existence for the 3D Tropical Climate Model with Small Initial Data in H˙1/2ℝ3∗ by Hui Zhang, Juan Xu

“…The well-posedness problem is an important but challenging research topic in nonlinear partial differential equations. In this paper, we establish a global-in-time existence result of strong solutions for small initial data in terms of the H˙1/2ℝ3 norm on three-dimensional tropical climate model with viscosities by derive a blow-up criterion combine with energy estimates. …”
Get full text

A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach by Taha Aziz, F. M. Mahomed

“…In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. …”
Get full text

Fractional-View Analysis of Space-Time Fractional Fokker-Planck Equations within Caputo Operator by Saleh Alshammari, Naveed Iqbal, Mohammad Yar

“…Compared to other methods of finding approximate and exact solutions for nonlinear partial differential equations, this technique is more efficient and time-consuming.…”
Get full text

Generalized Hyperbolic Function Solution to a Class of Nonlinear Schrödinger-Type Equations by Zeid I. A. Al-Muhiameed, Emad A.-B. Abdel-Salam

“…With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are investigated and the exact solutions are derived with the aid of the homogenous balance principle and generalized hyperbolic functions. …”
Get full text

On the Exact Solutions of Nonlinear Potential Yu–Toda–Sasa–Fukuyama Equation by Different Methods by Qinghao Zhu, Jianming Qi

“…It is observed that the extended complex method and G′/G-expansion method are reliable and will be used extensively to seek for exact solutions of any other nonlinear partial differential equations (NPDEs).…”
Get full text

Some new existence results of positive solutions for anisotropic variable exponent operator by Rafik Guefaifia, Salah Boulaaras, Rashid Jan

“…By deriving new existence results, the study advances the understanding of nonlinear partial differential equations in anisotropic and variable exponent settings. …”
Get full text

On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations by S. S. Motsa

“…This paper presents a new application of the homotopy analysis method (HAM) for solving evolution equations described in terms of nonlinear partial differential equations (PDEs). The new approach, termed bivariate spectral homotopy analysis method (BISHAM), is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. …”
Get full text

Approximate Solutions of Fisher's Type Equations with Variable Coefficients by A. H. Bhrawy, M. A. Alghamdi

“…Also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations.…”
Get full text

The General Traveling Wave Solutions of the Fisher Equation with Degree Three by Wenjun Yuan, Qiuhui Chen, Jianming Qi, Yezhou Li

“…Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.…”
Get full text

Influence of temperature-dependent viscosity on the MHD Couette flow of dusty fluid with heat transfer by Hazem A. Attia

“…The governing nonlinear partial differential equations are solved numerically and some important effects for the variable viscosity and the uniform magnetic field on the transient flow and heat transfer of both the fluid and dust particles are indicated.…”
Get full text

Constructions of solitary wave solutions for huge family of NPDEs with three applications. by Hanan A Alkhidhr, Y Omar

“…This study offers closed-form solutions for the frequently utilised families of nonlinear partial differential equations (NPDEs). This form based on the He's semi-inverse technique. …”
Get full text

Third-Order Approximate Solution of Chemical Reaction-Diffusion Brusselator System Using Optimal Homotopy Asymptotic Method by Salem Alkhalaf

“…The objective of this paper is to investigate the effectiveness and performance of optimal homotopy asymptotic method in solving a system of nonlinear partial differential equations. Since mathematical modeling of certain chemical reaction-diffusion experiments leads to Brusselator equations, it is worth demanding a new technique to solve such a system. …”
Get full text

On the derivation of the nonlinear discrete equations numerically integrating the Euler PDEs by F. N. Koumboulis, M. G. Skarpetis, B. G. Mertzios

“…The Euler equations, namely a set of nonlinear partial differential equations (PDEs), mathematically describing the dynamics of inviscid fluids are numerically integrated by directly modeling the original continuous-domain physical system by means of a discrete multidimensional passive (MD-passive) dynamic system, using principles of MD nonlinear digital filtering. …”
Get full text

Conservation Laws, Symmetry Reductions, and New Exact Solutions of the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation with Time-Dependent Coefficients by Li-hua Zhang

“…Applying the characteristic equations of the obtained symmetries, the (2 + 1)-dimensional KP equation is reduced to (1 + 1)-dimensional nonlinear partial differential equations, including a special case of (2 + 1)-dimensional Boussinesq equation and different types of the KdV equation. …”
Get full text

Travelling wave solutions to some PDEs of mathematical physics by Kourosh Nozari, Ghasem Alizadeh Afrouzi

“…As a result, some ambiguities arise when we want to solve nonlinear partial differential equations such as differential equations of elasticity and multifluid flows, or some new cosmological models such as signature changing space-times. …”
Get full text

A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations by E. H. Doha, D. Baleanu, A. H. Bhrawy, M. A. Abdelkawy

“…Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.…”
Get full text

New Exact Solutions of Kolmogorov Petrovskii Piskunov Equation, Fitzhugh Nagumo Equation, and Newell-Whitehead Equation by Yu-Ming Chu, Shumaila Javeed, Dumitru Baleanu, Sidra Riaz, Hadi Rezazadeh

“…This work presents the new exact solutions of nonlinear partial differential equations (PDEs). The solutions are acquired by using an effectual approach, the first integral method (FIM). …”
Get full text

Flow over Exponentially Stretching Sheet through Porous Medium with Heat Source/Sink by I. Swain, S. R. Mishra, H. B. Pattanayak

“…The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically using a fourth-order Runge-Kutta method with a shooting technique. …”
Get full text