Extractions of some new travelling wave solutions to the conformable Date-Jimbo-Kashiwara-Miwa equation

In this paper, complex and combined dark-bright characteristic properties of nonlinear Date-Jimbo-Kashiwara-Miwa equation with conformable are extracted by using two powerful analytical approaches. Many graphical representations such as 2D, 3D and contour are also reported. Finally, general conclusions of about the novel findings are introduced at the end of this manuscript

Numerical Analysis and Theory of Oblique Alfvenic Solitons Observed in the Interplanetary Magnetic Field

Recently, there have been reports of small magnetic pulses or bumps in the interplanetary magnetic field observed by various spacecraft. Most of these reports claim that these localized pulses or bumps are solitons. Solitons are weakly nonlinear localized waves that tend to retain their form as they propagate and can be observed in various media which exhibit nonlinear steepening and dispersive effects. This thesis expands the claim that these pulses or bumps are nonlinear oblique Alfven waves with soliton components, through the application of analytical techniques used in the inverse scattering transform in a numerical context and numerical integration of nonlinear partial dierential equations. One event, which was observed by the Ulysses spacecraft on February 21st, 2001, is extensively scrutinized through comparison with soliton solutions that emerge from the Derivative Nonlinear Schrodinger (DNLS) equation. The direct scattering transform of a wave prole that has corresponding morphology to the selected magnetic bump leads to the implication of a soliton component. Numerical integration of the scaled prole matching the event in the context of the DNLS leads to generation of dispersive waves and a one parameter dark soliton

Selected Topics in Plasma Physics

This book is planned to introduce the advances topics of plasma physics for research scholars and postgraduate students. This book deals with basic concepts in plasma physics, non-equilibrium plasma modeling, space plasma applications, and plasma diagnostics. It also provides an overview of the linear and nonlinear aspects of plasma physics. Chapters cover such topics as plasma application in space propulsion, microwave–plasma interaction, plasma antennas, solitary waves, and plasma diagnostic techniques

Lie symmetry analysis, exact solutions and conservation laws for the time fractional modified Zakharov–Kuznetsov equation

In this work, Lie symmetry analysis (LSA) for the time fractional modified Zakharov–Kuznetsov (mZK) equation with Riemann–Liouville (RL) derivative is analyzed. We transform the time fractional mZK equation to nonlinear ordinary differential equation (ODE) of fractional order using its point symmetries with a new dependent variable. In the reduced equation, the derivative is in Erdelyi–Kober (EK) sense. We obtained exact traveling wave solutions by using fractional DξαG/G-expansion method. Using Ibragimov's nonlocal conservation method to time fractional nonlinear partial differential equations (FNPDEs), we compute conservation laws (CLs) for the mZK equation

Nonlinear Lattice Dynamics of Bose-Einstein Condensates

The Fermi-Pasta-Ulam (FPU) model, which was proposed 50 years ago to examine thermalization in non-metallic solids and develop ``experimental'' techniques for studying nonlinear problems, continues to yield a wealth of results in the theory and applications of nonlinear Hamiltonian systems with many degrees of freedom. Inspired by the studies of this seminal model, solitary-wave dynamics in lattice dynamical systems have proven vitally important in a diverse range of physical problems--including energy relaxation in solids, denaturation of the DNA double strand, self-trapping of light in arrays of optical waveguides, and Bose-Einstein condensates (BECs) in optical lattices. BECS, in particular, due to their widely ranging and easily manipulated dynamical apparatuses--with one to three spatial dimensions, positive-to-negative tuning of the nonlinearity, one to multiple components, and numerous experimentally accessible external trapping potentials--provide one of the most fertile grounds for the analysis of solitary waves and their interactions. In this paper, we review recent research on BECs in the presence of deep periodic potentials, which can be reduced to nonlinear chains in appropriate circumstances. These reductions, in turn, exhibit many of the remarkable nonlinear structures (including solitons, intrinsic localized modes, and vortices) that lie at the heart of the nonlinear science research seeded by the FPU paradigm.Comment: 10 pages, revtex, two-columns, 3 figs, accepted fpr publication in Chaos's focus issue on the 50th anniversary of the publication of the Fermi-Pasta-Ulam problem; minor clarifications (and a couple corrected typos) from previous versio