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Analysis of optical solutions of higher-order nonlinear Schrödinger equation by the new Kudryashov and Bernoulli’s equation approaches
The optical soliton solutions of the time-fractional higher-order nonlinear Schrödinger equation in the presence of the Kudryashov nonlinear...
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Diverse soliton structures for fractional nonlinear Schrodinger equation, KdV equation and WBBM equation adopting a new technique
Nonlinear fractional evolution equations are significant models for depicting intricate physical phenomena arise in nature. In this exploration, we...
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Stellar Evolution, SN Explosion, and Nucleosynthesis
Massive stars evolve toward the catastrophic collapse of their innermost core, producing core-collapse supernova (SN) explosions as the end products....
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Long-Term Evolution of the Saturnian System
Here we present the current state of knowledge on the long-term evolution of Saturn’s moon system due to tides within Saturn. First we provide some...
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Darwinian Evolution, Hypercycles and Game Theory
Adaptation and evolution are quasi synonymous in popular language, it is hence little surprising that the theory of Darwinian evolution is infused...
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Akhmediev and Kuznetsov–Ma rogue wave clusters of the higher-order nonlinear Schrödinger equation
In this work, we analyze three types of rogue wave (RW) clusters for the quintic nonlinear Schrödinger equation (QNLSE) on a flat background. These...
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Soliton solutions for a (3 + 1)-dimensional nonlinear integrable equation
In order to obtain the local structural solutions of nonlinear integrable systems, a (3 + 1)-dimensional nonlinear integrable equation is studied by...
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Boltzmann Equation and the H-Theorem
Although the formula engraved on Boltzmann’s tombstone is Eq. ( 8.1 ), connecting the entropy of a...
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Integration of negative-order modified Korteweg–de Vries equation in a class of periodic functions
AbstractWe study the negative-order modified Korteweg–de Vries equation and show that it can be integrated by the inverse spectral transform...
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Langevin Equation and Brownian Dynamics Simulations
In this chapter, we aim to elucidate the details behind writing computational codes and running a Brownian dynamics simulations (BDSs). Given that...
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Exploring exact solitary wave solutions of Kuralay-II equation based on the truncated M-fractional derivative using the Jacobi Elliptic function expansion method
This paper focuses on the Kuralay-II equation, a prominent nonlinear evolutionary equation used in various scientific fields. Our goal was to...
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Colour evolution and infrared physics
We give a complete account of how soft gluon, massless quark, evolution equations in colour space originate, from a factorization into a hard cross...
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Stability analysis, lump and exact solutions to Sharma–Tasso–Olver–Burgers equation
In this work, the Hirota bilinear symbolic computational method along with test functions and the generalized exponential rational function method...
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Nonlinear dynamics of the generalized unstable nonlinear Schrödinger equation: a graphical perspective
In this work, the generalized unstable nonlinear Schrödinger equation is examined, which is used to predict the temporal evolution of disturbances in...
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A Novel Investigation on Propagation of Envelop Optical Soliton Structure Through a Dispersive Medium in the Nonlinear Whitham–Broer–Kaup Dynamical Equation
The nonlinear Whitham-Broer-Kaup dynamical equation under investigation on the base of auxiliary equation approach. We secured the exact soliton...
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Smoothness of Solutions of the Eikonal Equation and Regular Points of Their Level Surfaces
AbstractProperties of local solarity and regularity in essentially asymmetric locally uniformly rotund spaces are studied. The results obtained are...
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Stability, modulation instability, and analytical study of the confirmable time fractional Westervelt equation and the Wazwaz Kaur Boussinesq equation
This study delves into the analytical exploration of two pivotal equations, the confirmable Westervelt equation, relevant in acoustic nonlinear...
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Multiple mixed solutions of the nonlocal sine-Gordon equation
In this paper, we propose the nonlocal sine-Gordon equation from the AKNS system by the Parity and the Time symmetries. Moreover, the main work is to...
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Cosmological Evolution with Negative Energy Densities
For general number of spatial dimensions we investigate the cosmological dynamics driven by a cosmological constant and by a source with barotropic...
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Hirota bilinear method for nonlinear evolution equations
The bilinear method introduced by Hirota to obtain exact solutions for nonlinear evolution equations is discussed. Firstly, several examples...