Wide classes of nonlinear mathematical physics equations are described that admit order reduction through the use of the Crocco transformation, with a first-order partial derivative taken as a new independent variable and a second-order partial derivative taken as the new dependent variable. Associated Bäcklund transformations are constructed for evolution equations of general form (special cas...

We analyze the derivative nonlinear Schrödinger equation iqt + qxx = i ( |q|q ) x on the half-line using the Fokas method. Assuming that the solution q(x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter ζ. The jump matrix has explicit x, t dependence and is given in terms of the ...

A generalized derivative nonlinear Schrödinger equation, iqt + qxx + 2iγ|q| qx + 2i(γ − 1)q q x + (γ − 1)(γ − 2)|q| q = 0, is studied by means of Hirota’s bilinear formalism. Soliton solutions are constructed as quotients of Wronski-type determinants. A relationship between the bilinear structure and gauge transformation is also discussed. ∗e-mail: [email protected] §

The construction of some without memory efficient sixth-order iterative schemes for solving univariate nonlinear equations is presented. Per iteration, the novel methods comprise four evaluations of the function, while they are free from derivative calculations. The application of such iterative methods is appeared, when the cost of derivative evaluation is expensive. We analytically show the s...

We study the initial-boundary value problem for the derivative nonlinear Schrödinger (DNLS) equation. More precisely we study the wellposedness theory and the regularity properties of the DNLS equation on the half line. We prove almost sharp local wellposedness, nonlinear smoothing, and small data global wellposedness in the energy space. One of the obstructions is that the crucial gauge transf...

Considering the magneto-hydrodynamic equations in a non-relativistic multi uid framework, we study the behavior of small amplitude perturbations in cold quark matter. Magneto-hydrodynamic equations, along with a suitable equation of state for the cold quark matter, are expanded using the reductive perturbation method. It is shown that in small amplitude approximation, such a medium should be co...

in this study, based on the optimal free derivative without memory methods proposed by cordero et al. [a. cordero, j.l. hueso, e. martinez, j.r. torregrosa, generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation, mathematical and computer modeling. 57 (2013) 1950-1956], we develop two new iterative with memory methods for solving a nonline...

Nonlinear fractional differential equations have gained a significant place in mathematical physics. Finding the solutions to these has emerged as field of study that attracted lot attention lately. In this work, He’s semi-inverse variation method and ansatz been applied find soliton for Korteweg–de Vries equation, equal width modified equation defined by Atangana’s conformable derivative (beta...