The Boussinesq equation simulates weakly nonlinear and long wave approximation that can be used in water waves, coastal engineering, numerical models for simulation harbors shallow seas. In this article, the sine-Gordon expansion (SGE) approach generalized Kudryashov (GK) scheme are to establish broad-spectral solutions including unknown parameters typical analytical recovered as a special case. well-known bell-shape soliton, kink, singular compacton, contracted periodic anti-bell shape...

This paper studies the optical soliton solutions of a nonlinear Schrödinger equation (NLSE) involving parabolic law nonlinearity with presence dispersion by using generalized auxiliary technique. As result, new varieties exact traveling wave have been uncovered, comprising hyperbolic trigonometric, exponential, and rational. Interestingly, we obtain bright, dark, periodic, singular, other to model. Some achieved are illustrated graphically in order fully understand their physical behaviour....

In the field of nonlinear optics, quantum mechanics, condensed matter physics, and wave propagation in rigid other instability phenomena, Schrödinger equation has significant applications. this study, soliton solutions space-time fractional cubic with Kerr law nonlinearity are investigated using an extended direct algebraic method. The found form hyperbolic, trigonometric, rational functions. Among established solutions, some exhibit wide spectral typical characteristics, while others...

A conserved insulin-like pathway modulates both aging and pathogen resistance in Caenorhabditis elegans . However, the specific innate effector functions that mediate this are largely unknown. Autophagy, a lysosomal degradation pathway, plays role controlling intracellular bacterial infections cultured cells, but less is known about its at organismal level. We examined effects of autophagy gene inactivation on Salmonella enterica Serovar Typhimurium ( typhimurium ) infection 2 model...

The modified simple equation (MSE) method is thriving in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) engineering and mathematical physics. In this study, we bring to bear the MSE look for via Tzitzeica–Dodd–Bullough KdV–Zakharov–Kuznetsov involving parameters. When parameters receive special values, solitary are derived from solutions. By means scheme, found some fresh above mentioned equations.

We construct new analytical solutions of the (3 + 1)‐dimensional modified KdV‐Zakharov‐Kuznetsev equation by Exp‐function method. Plentiful exact traveling wave with arbitrary parameters are effectively obtained The results show that method is effective and straightforward mathematical tool for searching higher‐dimensional nonlinear partial differential equation.

A generalized and improved ( G ′ / )‐expansion method is proposed for finding more general type new travelling wave solutions of nonlinear evolution equations. To illustrate the novelty advantage method, we solve KdV equation, Zakharov‐Kuznetsov‐Benjamin‐Bona‐Mahony (ZKBBM) equation strain in microstructured solids. Abundant exact these equations are obtained, which include soliton, hyperbolic function, trigonometric rational functions. Also it shown that efficient solving mathematical...

In this article, a novel (G'/G)-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant involving parameters Boussinesq equation by means suggested method. The performance reliable and useful, gives more general exact than existing methods. new provides not only forms but also cuspon, peakon, soliton, periodic waves.

In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via improved (G ' /G)-expansion method. The are presented in terms of trigonometric, hyperbolic, and rational functions. When take special values, solitary waves derived from waves.

In this article, the exp(−Φ(ξ))-expansion method has been successfully implemented to seek traveling wave solutions of coupled Higgs field equation and Maccari system. The result reveals that together with first order ordinary differential is a very influential effective tool for solving nonlinear partial equations in mathematical physics engineering. obtained have articulated by hyperbolic functions, trigonometric functions rational arbitrary constants. Numerical results graphical...

The (3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications theory of long-wave propagation, dynamics shallow water wave, plasma fluid model, chemical kinematics, engineering, geochemistry, many other topics. In this article, we assessed effects wave speed physical parameters on contours confirmed that waveform changes with variety free factors it. As result, solutions are...

The perturbed nonlinear Schrödinger–Hirota equation with spatio-temporal dispersion (PNSHE-STD) which governs the propagation of dispersive pulses in optical fibers, is investigated this study using an improved Sardar sub-equation method. Kerr and power laws nonlinearity are taken into account. As a result technique, many constraint conditions required for existence soliton solutions emerge. We retrieved several such as bright solitons, dark singular mixed bright–dark singular-bright combo...

In this survey, structure solutions for the longitudinal suspense equation within a magneto-electro-elastic (MEE) circular judgment are extracted via implementation of two one-of-a-kind techniques that viewed as close generalized technique in its field. This paper describes dynamics MEE round rod. Nilsson and Lindau provided visual proof arrival concerning waves thin metal films. They recommended removal anomalies between ports emaciated ([Formula: see text] Å) Ag layers preserved on...

The perturbed nonlinear Schrödinger (NLS) equation and the radial dislocations model in microtubules (MTs) are underlying frameworks to simulate dynamic features of solitons optical fibers functional aspects microtubule dynamics. generalized Kudryashov method is used this article extract stable, generic, wide-ranging soliton solutions, comprising hyperbolic, exponential, trigonometric, some other functions, retrieve diverse known structures by balancing effects nonlinearity dispersion. It...

It becomes an interesting part for the researchers to analyze dynamical behavior of soliton propagation in optical fibers trans-oceanic and trans-continental distances. In this paper, we desire retrieve distinct innovative accurate wave solutions dual core fiber nonlinear equations by adopting improved tanh method rational [Formula: see text]-expansion method. Consequently, a bundle is achieved diverse sense. The acquired are made visible profiles three-dimensional (3D), two-dimensional (2D)...

For uni-directional wave transmission in the smooth bottom of shallow sea water and superconductivity nonlinear media with dispersion systems, (1 + 1)-dimensional Camassa-Holm Landau-Ginzburg-Higgs equations are particular interest research to academics. Analytical solutions stated models have been successfully constructed this study, which might considerable implications describing dynamical behavior associated phenomena. The we aim uncover put into form differential one characteristic...

The Chen-Lee -Liu model has many applications in assorted fields, particularly the study of nonlinear dynamics, chaos theory, circuit design, signal processing, secure communications, encryption and decryption chaotic signals, as well cryptography. modified extended auxiliary equation mapping method been applied to Chen-Lee-Liu this article explores new wave profiles, such singular periodic solutions, kink-type soliton solutions. complex conversion is considered make a simple differential...

The key traits of optical fiber and plasma physics are interpreted by the typical space-time fractional nonlinear perturbed Chen-Lee-Liu equation. equation is regarded in sense beta derivative, a composite wave transformation used to reshape it into single variable. This article aims compute diverse analytical soliton solutions through potential (G′/G,1/G)-expansion approach. include periodic soliton, bell-shaped anti-peakon, V-shaped compacton, others that might be supportive analyze signal...

In this study, the closed-form wave solutions has been examined to space–time fractional simplified Camassa-Holm equation through two potential techniques, namely sine-Gordon expansion approach and extended tanh function scheme. The explains dispersion effects of several phenomena, including liquid drop patterning in plasma, fluid flow, fission fusion processes, acoustics, control theory, etc. fractional-order is transformed into a nonlinear complex transformation. Diverse are determined,...

Abstract In this pioneering study, we have systematically derived traveling wave solutions for the highly intricate Zoomeron equation, employing well-established mathematical frameworks, notably modified (G′/G)-expansion technique. Twenty distinct been revealed, each distinguished by distinguishable characteristics in domains of hyperbolic, trigonometric, and irrational expressions. Furthermore, used formidable computational capabilities Maple software to construct depictions these...

The modified simple equation (MSE) method is promising for finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. In this letter, we investigate the (2 + 1)-dimensional Zoomeron and Burgers by using MSE Exp-function method. competence methods constructing has been established.

The modified simple equation (MSE) method is a competent and highly effective mathematical tool for extracting exact traveling wave solutions to nonlinear evolution equations (NLEEs) arising in science, engineering physics. In this article, we implement the MSE find involving parameters NLEEs via Benney–Luke Phi-4 equations. solitary are derived from when receive their special values.

In recent years, searching exact traveling wave solutions to nonlinear evolution equations (NLEEs) has become a remarkable topic of research. this article, we obtain two significant NLEEs, namely, the PHI-four equation and Fisher involving parameters by using generalized Kudryashov method. We attain some exponential type including kink soliton, bisymmetry periodic solution when receive different values. provide graphical representations respective also.