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We calculate large mass diphoton exclusive photoproduction in the framework of collinear QCD factorization at next to leading order in {\alpha}s and at leading twist. Collinear divergences of the coefficient function are absorbed by the…

High Energy Physics - Phenomenology · Physics 2021-08-02 Oskar Grocholski , Bernard Pire , Paweł Sznajder , Lech Szymanowski , Jakub Wagner

Large set of linear equations, especially for sparse and structured coefficient (matrix) equations, solutions using classical methods become arduous. And evolutionary algorithms have mostly been used to solve various optimization and…

Neural and Evolutionary Computing · Computer Science 2013-04-16 A. R. M. Jalal Uddin Jamali , M. M. A. Hashem , Md. Bazlar Rahman

The Petviashvili's iteration method has been known as a rapidly converging numerical algorithm for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power-law nonlinearity: \ $-Mu+u^p=0$, where…

Pattern Formation and Solitons · Physics 2009-11-13 T. I. Lakoba , J. Yang

In this paper we explore the possibility for solving the 3D Maxwell's equations in the presence of nonlinear and/or inhomogeneous material response. We propose using a hybrid approach which combines a bound- ary integral representation with…

Numerical Analysis · Mathematics 2019-08-07 Aihua Lin , Per Kristen Jakobsen

In this paper the Levy-Leblond procedure for linearizing the Schr\"odinger equation to obtain the Pauli equation for one particle is generalized to obtain an $N$-particle equation with spin. This is achieved by using the more universal…

Quantum Physics · Physics 2007-05-23 Irving S. Reed , Todd A. Brun

We use a fractional transformation to connect the traveling wave solutions of the nonlinear Schr\"odinger equation (NLSE), phase-locked with a source, to the elliptic functions satisfying, $f^{\prime\prime}\pm af\pm \lambda f^{3}=0$. The…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 T. Soloman Raju , C. Nagaraja Kumar , Prasanta K. Panigrahi

In this work we present an application of a theory of vessels to solution of the evolutionary Non Liner Schrodinger (NLS) equation. The classes of functions for which the initial value problem is solvable relies on the existence of an…

Analysis of PDEs · Mathematics 2014-11-04 A. Melnikov

We describe a variant of the dressing method giving alternative representation of multidimensional nonlinear PDE as a system of Integro-Differential Equations (IDEs) for spectral and dressing functions. In particular, it becomes single…

Analysis of PDEs · Mathematics 2016-09-07 A. I. Zenchuk

With a view to having further insight into the mathematical content of the non-Hermitian Hamiltonian associaterd with the diffusion-reaction (D-R) equation in one dimension, we investigate (a) the solitary wave solutions of certain types of…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 R. S. Kaushal

In this paper, we introduce a Fourier-type formalism on non-commutative spaces. As a result, we obtain two versions of Hormander-Mikhlin Lp-multiplier theorem: on locally compact Kac groups and on semi-finite von Neumann algebras,…

Operator Algebras · Mathematics 2026-03-10 Rauan Akylzhanov , Michael Ruzhansky , Kanat Tulenov

An efficient method to construct Hamiltonian structures for nonlinear evolution equations is described. It is based on the notions of variational Schouten bracket and l*-covering. The latter serves the role of the cotangent bundle in the…

Differential Geometry · Mathematics 2010-04-09 Paul Kersten , Iosif Krasil'shchik , Alexander Verbovetsky

We show that the complex modified KdV (cmKdV) equation and generalized nonlinear Schr\"odinger (GNLS) equation belong to the Ablowitz, Kaup, Newell and Segur or so-called AKNS hierarchy. Both equations do not follow from the action…

Exactly Solvable and Integrable Systems · Physics 2009-06-30 Debabrata Pal , Amitava Choudhuri , B Talukdar

Starting from a comparison of some established numerical algorithms for the computation of the eigenvalues (discrete or solitonic spectrum) of the non-Hermitian version of the Zakharov-Shabat spectral problem, this article delivers new…

Numerical Analysis · Mathematics 2018-09-11 A. Vasylchenkova , J. E. Prilepsky , D. Shepelsky , A. Chattopadhyay

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…

Exactly Solvable and Integrable Systems · Physics 2023-04-14 Metin Gürses , Aslı Pekcan

Motivated by the regime of QCD explored nowadays at LHC, where both the total energy of collision and momenta transfers are high, we investigate evolution equations of high energy factorization. In order to study such effects like parton…

High Energy Physics - Phenomenology · Physics 2012-04-13 Krzysztof Kutak , Krzysztof Golec-Biernat , Stanislaw Jadach , Maciej Skrzypek

In this paper, we derive a B\"{a}cklund transformation for the supersymmetric Kortweg-de Vries equation. We also construct a nonlinear superposition formula, which allows us to rebuild systematically for the supersymmetric KdV equation the…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 Q. P. Liu , Y. F. Xie

We proposed in this paper a new method, which we named the W4 method, to solve nonlinear equation systems. It may be regarded as an extension of the Newton-Raphson~(NR) method to be used when the method fails. Indeed our method can be…

Numerical Analysis · Mathematics 2022-04-22 Hirotada Okawa , Kotaro Fujisawa , Yu Yamamoto , Nobutoshi Yasutake , Misa Ogata , Shoichi Yamada

In this paper we apply Kahan's nonstandard discretization to three dimensional Lotka-Volterra equations in bi-Hamiltonian form. The periodicity of the solutions and all polynomial and non-polynomial invariants are well preserved in…

Numerical Analysis · Mathematics 2025-06-23 Murat Uzunca

The objective of this work is to explore the class of equations of the Non-linear Schrodinger type by employing the Adler-Kostant-Symes theorem and the Tu methodology.In the first part of the work, the AKS theory is discussed in detail…

Exactly Solvable and Integrable Systems · Physics 2014-05-23 Partha Guha , Indranil Mukherjee

We study standard and nonlocal nonlinear Schr\"{o}dinger (NLS) equations obtained from the coupled NLS system of equations (Ablowitz-Kaup-Newell-Segur (AKNS) equations) by using standard and nonlocal reductions respectively. By using the…

Exactly Solvable and Integrable Systems · Physics 2018-06-28 Metin Gürses , Aslı Pekcan