Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation by V. O. Vakhnenko, E. J. Parkes

“…The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE), by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. …”
Get full text

Explicit solutions of nonlocal reverse-time Hirota-Maxwell-Bloch system by Zh. Myrzakulova, Z. Zakariyeva, K. Suleimenov, U. Uralbekova, K. Yesmakhanova

“…In this paper, we investigate the nonlocal reverse-time Hirota-Maxwell-Bloch system, focusing on its soliton solutions using the Darboux transformation method. …”
Get full text

Noncommutative Multisoliton Solutions of a Supersymmetric Chiral Model by Xiujuan Zhu

“…These configurations have no-scattering property. A two-soliton configuration with nontrivial scattering was constructed soon after that. …”
Get full text

Multiple-Pole Solutions to a Semidiscrete Modified Korteweg-de Vries Equation by Zhixing Xiao, Kang Li, Junyi Zhu

“…The simplest multiple-pole soliton solution is presented. The dynamics of the solitons are studied.…”
Get full text

The Multisoliton Solutions for the (2+1)-Dimensional Sawada-Kotera Equation by Zhenhui Xu, Hanlin Chen, Wei Chen

“…Applying bilinear form and extended three-wavetype of ansätz approach on the (2+1)-dimensional Sawada-Kotera equation, we obtain new multisoliton solutions, including the double periodic-type three-wave solutions, the breather two-soliton solutions, the double breather soliton solutions, and the three-solitary solutions. …”
Get full text

Bounded Traveling Wave Solutions and Their Relations for the Generalized HD Type Equation by Qing Meng, Bin He

“…From a dynamic point of view, the existence of different kinds of traveling waves which include periodic loop soliton, periodic cusp wave, smooth periodic wave, loop soliton, cuspon, smooth solitary wave, and kink-like wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given. …”
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

“…At the same time, many new exact solutions are derived such as soliton and soliton-like solutions and algebraically explicit analytical solutions.…”
Get full text

New Exact Traveling Wave Solutions of Fractional Time Coupled Nerve Fibers via Two New Approaches by Saud Owyed

“…In this paper, we obtain new soliton solutions of one of the most important equations in biology (fractional time coupled nerve fibers) using two algorithm schemes, namely, exp−ψξ expansion function method and θ′ξ/θ2ξ expansion methods. …”
Get full text

Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature by Yawei Chu, Dehe Li, Jundong Zhou

“…Let Mn,g,f be a complete gradient shrinking Ricci soliton of dimension n≥3. In this paper, we study the rigidity of Mn,g,f with pointwise pinching curvature and obtain some rigidity results. …”
Get full text

Modulation Instability, Analytical, and Numerical Studies for Integrable Time Fractional Nonlinear Model through Two Explicit Methods by Md. Mamunur Roshid, Mosfiqur Rahman, Mahtab Uddin, Harun Or Roshid

“…The main motivation of this work is to analyze modulation instability and soliton solution of the time-fractional K-G model. …”
Get full text

Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method by Haifa Bin Jebreen

“…Different kinds of traveling wave solutions such as solitary, topological, dark soliton, periodic, kink, and rational are obtained as a by product of this scheme. …”
Get full text

CTE Solvability, Nonlocal Symmetry, and Interaction Solutions of Coupled Integrable Dispersionless System by Jun Yu, Bo Ren, Ping Liu, Jia-Li Zhou

“…Many interactions between one soliton and multiple resonant solitons, and between one soliton and cnoidal waves are generated by using the nonauto-BT theorem. …”
Get full text

Modulation Instability and Dynamical Analysis of New Abundant Closed-Form Solutions of the Modified Korteweg–de Vries–Zakharov–Kuznetsov Model With Truncated M-Fractional Derivativ... by Md. Shafiqul Islam, Md. Mamunur Roshid, Mahtab Uddin, Ashek Ahmed

“…In this work, we study the modulation instability (MI) and closed-form soliton solution of the modified Korteweg–de Vries–Zakharov–Kuznetsov (mKdV-ZK) equation with a truncated M-fractional derivative. …”
Get full text

High-Order Breather Solutions, Lump Solutions, and Hybrid Solutions of a Reduced Generalized (3 + 1)-Dimensional Shallow Water Wave Equation by Jing Wang, Biao Li

“…Based on Hirota’s bilinear method, the expression of N-soliton wave solutions is derived. By using the resulting N-soliton expression and reasonable constraining parameters, we concisely construct the high-order breather solutions, which have periodicity in x,y-plane. …”
Get full text

Application of Functional Variable Method for Heisenberg Ferromagnetic Spin Chain Equation by ALI TOZAR, Orkun Taşbozan, ALI KURT

“…Due to nonlinear interactions inherent in the model, soliton solutions that can be obtained have attracted the attention of mathematicians, in recent decades. …”
Get full text

Anomalous scattering of lumps for the extended Kadomtsev–Petviashvili equation arising in water wave by Haifang Song, Bo Ren

“…The asymptotic approach can give the interaction between anomalously scattered lumps and a soliton apart from the interaction between lumps. …”
Get full text

On quasi-integrable deformation scheme of the KdV system by Kumar Abhinav, Partha Guha

“…(Nucl Phys B 939:49–94, 2019), that are particular cases of the present approach, general soliton solutions should numerically be accessible.…”
Get full text

Analytic Solutions of 2D Cubic Quintic Complex Ginzburg-Landau Equation by F. Waffo Tchuimmo, J. B. Gonpe Tafo, A. Chamgoue, N. C. Tsague Mezamo, F. Kenmogne, L. Nana

“…For some parameters, one has the orbits starting to one fixed point and passing through another fixed point before returning to the same fixed point, predicting then the existence of the combination of a pair of pulse-dark soliton. One has also for other parameters, the orbits linking three equilibrium points predicting the existence of a dark soliton pair. …”
Get full text

Nonlocal Symmetry, CRE Solvability, and Exact Interaction Solutions of the (2 + 1)-Dimensional Boussinesq Equation by Sixing Tao

“…Three special forms of soliton-cnoidal wave interaction solutions are discussed analytically and shown graphically.…”
Get full text

A Riemann-Hilbert Approach to the Multicomponent Kaup-Newell Equation by Jian-bing Zhang, Ze-xuan Zhang

“…The formula is presented of N-soliton solutions through an identity jump matrix related to the inverse scattering problems with reflectionless potential.…”
Get full text