In this article, the magnetohydrodynamic (MHD) thermal boundary layer of a Carreau flow Cu-water nanofluids over an exponentially permeable stretching thin plate is investigated numerically. Internal heat source/sink also taken into account. After gaining system leading equations, appropriate transformations have been first employed to come across fitting parallel conversions alter central governing equations suit ODEs and then renovated ODE along with conditions numerically solved by...

In this paper, the cubic-quartic nonlinear Schrödinger and resonant equation in parabolic law media are investigated to obtain dark, singular, bright-singular combo periodic soliton solutions. Two powerful methods, m + G ′ improved expansion method exp − φ ξ utilized construct some novel solutions of governing equations. The obtained optical presented graphically clarify their physical parameters. Moreover, verify existence solutions, constraint conditions utilized.

In this work, N-soliton waves, fusion solutions, mutiple M-lump solutions and the collision phenomena between one-M-lump one-, two-soliton to (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation are successfully revealed. A class of two-, three-soliton, two-fusion derived via Hirota bilinear method 1-M-lump, 2-M-lump constructed long-wave method. Moreover, physical phenomenon 1-M-lump with also, presented. The velocity wave in x- y-direction also studied.

This study deals the dynamics of waves to conformable fractional (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equations. The NNV equations are isotropic Lax integrable extension (1+1)-dimensional Korteweg–de Vries Fractional differential models (FDMs) from corresponding integer order model can describes more complex behavior and even cover all properties model. By usage different test approaches, Hirota bilinear method (HBM) has been successfully applied. is a well-known reliable...

In this paper, we use the modified auxiliary expansion method to seek some new solutions of paraxial nonlinear Schrödinger equation. The have a hyperbolic function, trigonometric exponential and rational function forms linear stability analysis NLSE is also presented study modulational instability (MI). Two cases when modulation becomes occur are investigated. Depending on MI cases, gain spectrum investigated graphically. All verified main equation wave Moreover, constraint conditions for...

In this paper, we use the modified exponential function method in terms of 𝐾𝑓(𝑥) instead 𝑒𝑓(𝑥) and extended sinh-Gordon to find some new family solution M-fractional paraxial nonlinear Schrödinger equation. The novel complex real optical soliton solutions are plotted 2-D, 3-D with a contour plot. Moreover, dark exact solution, singular solutions, kink-type periodic dark-singular for equation constructed. We guarantee that all verified main wave For existence, constraint condition is also added.

<abstract> In this paper, the modified auxiliary expansion method is used to construct some new soliton solutions of coupled Schrödinger-Boussinesq system that includes beta derivative. The exact solution obtained have a hyperbolic function, trigonometric exponential and rational function. These might appreciate in laser plasma sciences. It shown method, provides straightforward powerful mathematical tool for solving nonlinear problems. Moreover, linear stability analyzed. </abstract>

One of the most effective ways to understand nonlinear quantum systems is with lump solutions. The objective this study acquire more about (3+1)-dimensional soliton equation. We successfully present equation various solitons and M-lump adopt specific parameter values accentuate physical features provided exact solutions through 3D contour plots as doing so extreme significance. submitted results indicate qualities lump-and-lump interaction events in processes.

In this study, we focus on the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili (gBKP) equation in fluid dynamics, which is useful for modeling weakly dispersive waves transmitted quasi media and mechanics. As a general matter, paper examines gBKP including variable coefficients of time that are widely employed plasma physics, marine engineering, ocean nonlinear sciences to explain shallow water waves. Using Hirota’s bilinear approach, one-, two, three-soliton solutions problem...

In the present work, we employed a novel modification of Sardar sub-equation approach, leading to successful derivation several exact solutions for time-fractional Ginzburg–Landau equation with Kerr law nonlinearity. These encompass range categories, including singular, wave, bright, mixed dark-bright, and bell-shaped optical solutions. We demonstrate dynamic behavior physical significance these proposed model via graphical simulations, contour plots, three-dimensional (3D) graphs,...

The multiple Exp-function method is employed for searching the soliton solutions new extended (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>)-dimensional Jimbo-Miwa-like (JM) equation, id="M2"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>)-dimensional Calogero-Bogoyavlenskii-Schiff (eCBS) generalization of...

In this study, we investigate the (2 + 1)-dimensional Korteweg-De Vries (KdV) equation with extension of time-dependent coefficients. A symbolic computational method, simplified Hirota's and a long-wave method are utilized to create various exact solutions suggested equation. The is applied Lump periodic lump waves. implemented explore single-, double- triple-M-lump waves, interaction physical phenomena such as an single-M-lump one-, two-soliton solutions, well collision double-M-lump...

In this work, the Date–Jimbo–Kashiwara–Miwa (DJKM) equation include time-dependent in (2+1)-dimensions that characterize propagation of nonlinear dispersive waves inhomogeneous media is studied. We construct rational solutions and interaction physical phenomena between solution multi-soliton wave to DJKM equation. The are revealed by using Hirota simple method, then via long-wave M-lump for two types derived. Moreover, single-, double-soliton