19 papers · ranked by Valyu relevance
Chatterjee, Supriya, Sarkar, Pranab + 2 more
We introduce the concept of soliton solutions of integrable nonlinear partial differential equations and point out that the inverse spectral method represents the rigorous mathematical formalism to construct such solutions. We work with the travelling waves of the KdV, mKdV and nonlinear Schr¨odinger (NLS) equations…
Metin Gürses, Aslı Pekcan
Bilinearization of a given nonlinear partial differential equation is very important not only to find soliton solutions but also to obtain other solutions such as the complexitons, positons, negatons, and lump solutions. In this work we study the bilinearization of nonlinear partial differential equations in (2 +…
Samoilenko Valerii, Samoilenko Yuliia
The paper deals with a problem of asymptotic soliton-like solutions to the Benjamin–Bona–Mahony (BBM) equation with a small parameter at the highest derivative and variable coefficients depending on the variables x, t as well as a small parameter. An algorithm for constructing solutions to the BBM equation has been…
Rathinavel Silambarasan, Adem Kılıçman
The nonlinear dispersive wave equation inside the cylindrical elastic rod is derived by applying the Navier-Bernoulli hypothesis and Love's relation in [5]. The elastic rod is assumed to be composed of the Murnaghan's materials such as Lam ´e's coefficent, Poisson ratio and constitutive constant which are compressible…
Saima Arshed, Ghazala Akram, Maasoomah Sadaf, Komal Saeed + 1 more
'Shou-Fu Tian'] Korteweg-de Vries Caudrey-Dodd-Gibbon (KdV-CDG) equation describes many physical phenomena in plasma physics, optical fibers, dynamics of the ocean, quantum mechanics, acoustic waves and laser optical applications. In this paper, the KdV-CDG equation is analyzed via two reliable and efficient…
Yair Zarmi
Given a nonlinear evolution equation in (1+n) dimensions, which has spatially extended traveling wave solutions, it can be extended into a system of two coupled equations, one of which generates the original traveling waves, and the other generates structures that are localized in the vicinity of the intersections of…
Swapan K. Ghosh, Debabrata Pal, Aparna Saha, B. Talukdar
The traditional method of factorization can be used to obtain only the particular solutions of the Liénard type ordinary differential equations. We suggest a modification of the approach that can be used to construct general solutions . We first demonstrate the effectiveness of our method by dealing with a solvable…
Zong‐Wei Xu, Guo‐Fu Yu, Yik‐Man Chiang
Two integrable differential-difference equations are derived from a (2+1)-dimensional modified Heisenberg ferromagnetic equation and a resonant nonlinear Schr¨oinger equation respectively. Multi-soliton solutions of the resulted semi-discrete systems are given through Hirota's bilinear method. Elastic and inelastic…
A. M. Kamchatnov
We consider motion of a "magnetic" soliton in two-component condensates along a non-uniform and time-dependent backgrounds in framework of the Hamiltonian mechanics. Our approach is based on generalization of Stokes' remark that soliton's velocity is related with its inverse half-width by the dispersion law for linear…
Kamruzzaman Khan, M. Ali Akbar, H. Koppelaar
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of…
Muath Awadalla, Aigul Taishiyeva, Ratbay Myrzakulov, Jihan Alahmadi + 2 more
'Abdullah A. Zaagan' 'Ahmet Bekir'] In this paper we explore the new analytical soliton solutions of the truncated M-fractional nonlinear $1+1$-dimensional Akbota equation by applying the $\exp _a$ function technique, Sardar sub-equation and generalized kudryashov techniques. Akbota is an integrable equation which is…
Sheikh Zain Majid, Muhammad Imran Asjad, Muhammad Bilal Riaz, Taseer Muhammad + 1 more
'Taseer Muhammad' 'Muhammad Aqeel'] This article aims to study the time fractional coupled nonlinear Schrödinger equation, which explains the interaction between modes in nonlinear optics and Bose-Einstein condensation. The proposed generalized projective Riccati equation method and modified auxiliary equation method…
Miguel Vivas-Cortez, Saima Arshed, Maasoomah Sadaf, Zahida Perveen + 2 more
'Ghazala Akram' 'Shou-Fu Tian'] This article deals with studying the dynamical behavior of the DNA model proposed by Peyrard and Bishop. The proposed model is investigated using the unified method (UM). Unified method successfully extracts solutions in the form of polynomial and rational functions. The solitary wave…
Adil Jhangeer, Farheen Ibraheem, Tahira Jamal, Muhammad Bilal Riaz + 2 more
'Atef Abdel Kader' 'Boris Malomed'] Soliton dynamics and nonlinear phenomena in quantum deformation has been investigated through conformal time differential generalized form of q deformed Sinh-Gordon equation. The underlying equation has recently undergone substantial amount of research. In Phase 1, we employed…
Nauman Ahmed, Muhammad Z. Baber, Muhammad Sajid Iqbal, Amina Annum + 4 more
'Syed Mansoor Ali' 'Mubasher Ali' 'Ali Akgül' 'Sayed M. El Din'] In this study, the Lengyel-Epstein system is under investigation analytically. This is the reaction-diffusion system leading to the concentration of the inhibitor chlorite and the activator iodide, respectively. These concentrations of the inhibitor…
Siddhartha Sen
In this paper we show how both action potential-like soliton pulses and EEG-like waveform surface excitations can be generated by exploiting the topological connectivity properties of a hypothetical brain connectome, in a surface network, which we prove, exactly captures the topological architecture of any hypothetical…
Semen V. Nesterov, Lev S. Yaguzhinsky, Raif G. Vasilov, Vasiliy N. Kadantsev + 1 more
The results of many experimental and theoretical works indicate that after transport of protons across the mitochondrial inner membrane (MIM) in oxidative phosphorylation system (OXPHOS), they are retained on the membrane-water interface in non-equilibrium state with free energy excess due to low proton surface-to-bulk…
Shamit Shrivastava
Action potentials in neurons are known to annihilate each other upon collision, while there are cases where they might penetrate each other. Compression waves that travel within the plasma membrane of a neuron have previously been proposed as a thermodynamic basis for the propagation of action potentials. In this…
Nick Gorkavyi
Bimolecular cell membranes play a crucial role in many biological processes and possess a unique set of physical properties. Bimolecular membranes and monomolecular films can be considered as a “two-dimensional fluid” because the diffusion of molecules along the membrane or film is a hydrodynamic process. On the other…