Results 281 to 290 of about 16,555,549 (335)

First integrals and general solutions of the Biswas-Milovic equation

, 2020
The Biswas-Milovic equation for description of pulse propagation in optical fiber is considered. Solutions of the equation are looked for using the traveling wave reduction. The first integrals for a system of equations are found.
N. Kudryashov
semanticscholar   +1 more source

First integrals and general solution of the traveling wave reduction for Schrödinger equation with anti-cubic nonlinearity

Optik (Stuttgart), 2019
The traveling wave reduction of the Schrodinger equation with anti-cubic nonlinearity for describing of the optical solitons is studied. We find two first integrals of the system of equations corresponding to the real and imaginary part of the optical ...
N. Kudryashov
semanticscholar   +1 more source

First integrals and general solution of the Fokas–Lenells equation

Optik (Stuttgart), 2019
We consider the generalized Fokas–Lenells equation which has been become especially popular in recent years for the description soliton solutions in the optical fiber. This equation is studied by us using the traveling wave reduction.
N. Kudryashov
semanticscholar   +1 more source

Traveling wave reduction of the modified KdV hierarchy: The Lax pair and the first integrals

Communications in nonlinear science & numerical simulation, 2019
The traveling wave reduction of the modified Korteweg-de Vries hierarchy is considered. The linear system of equations associated with this hierarchy is found in the general form.
N. Kudryashov
semanticscholar   +1 more source

Lax pair and first integrals of the traveling wave reduction for the KdV hierarchy

Applied Mathematics and Computation, 2019
The traveling wave reduction of the Korteweg-de Vries hierarchy is considered. The linear system of equations associated with this hierarchy is found. The Lax pair is used to obtain the first integrals of the traveling wave reduction for the Korteweg-de ...
N. Kudryashov
semanticscholar   +1 more source

Nonautonomous first integrals and general solutions of the KdV‐Burgers and mKdV‐Burgers equations with the source

Mathematical methods in the applied sciences, 2019
The method for constructing first integrals and general solutions of nonlinear ordinary differential equations is presented. The method is based on index accounting of the Fuchs indices, which appeared during the Painlevé test of a nonlinear differential
N. Kudryashov, D. V. Safonova
semanticscholar   +1 more source

Symbolic Computations of First Integrals for Polynomial Vector Fields

Foundations of Computational Mathematics, 2017
In this article, we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for computing, if it exists, a rational, Darbouxian, Liouvillian or Riccati ...
Guillaume Chèze, Thierry Combot
semanticscholar   +1 more source

Elliptic Integrals of the First Kind

SIAM Journal on Mathematical Analysis, 1977
The reciprocal square root of any real polynomial with known zeros and degree not exceeding four is integrated in terms of a standard integral by a new quadratic transformation which preserves symmetry in the zeros. If at least one zero is real, this method, unlike earlier methods, leads to a single standard integral instead of a difference of two ...
openaire   +1 more source

On an integral equation of first kind

Siberian Mathematical Journal, 1991
In \(\mathbb{R}^3\) the family \(\Gamma\) of straight lines \(\xi_1 = x_1 + (\xi_3 - x_3) \cos \alpha\), \(\xi_2 = x_2 + (\xi_3 - x_3) \sin \alpha\), \(0 \leq \alpha \leq 2 \pi\), passing through the point \(x = (x_1, x_2, x_3)\), and the equation \[ \int_\Gamma u(\xi)d \ell + \int_{\mathbb{R}^3} \theta (k) \rho (\alpha, x, \xi) u(\xi)d \xi = v(x ...
openaire   +3 more sources

Integration of first- and second-order orientation

Journal of the Optical Society of America A, 2003
The problem of how visual information such as orientation is combined across space bears on key visual abiities, such as texture perception. Orientation signals can be derived from both luminance and contrast, but it is not well understood how such information is pooled or how these different orientation signals interact in the integration process.
Harriet A, Allen, Robert F, Hess, Behzad, Mansouri, Steven C, Dakin   +3 more
openaire   +2 more sources