Results 31 to 40 of about 9,068 (293)

BACKLUND TRANSFORMATIONS FOR LIOUVILLE’S EQUATIONS WITH EXPONENTIAL NONLINEARITY

Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020
Background. The study of Backlund 's transformations is one of the current topics in the theory of differential equations in partial derivatives. Such transformations are used to find solutions to nonlinear differential equations, including solitonic ...
T. V. Red'kina, O. V. Novikova
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SINGULAR SOLUTIONS OF CLAIRAUT-TYPE EQUATIONS IN PARTIAL DERIVATIVES WITH REVERSE TRIGONOMETRIC FUNCTIONS

Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020
Background. The problem of evaluation of the special (singular) solutions of Clairaut-type partial differential equations attracts a lot of interest studying various transformations of nonlinear equations of mathematical physics, for example, Legendre
L. L. Ryskina, A. S. Zubtsova, Yu. O. Shavenkova   +2 more
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A $$\overline{\partial }$$-dressing method for the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation

Journal of Nonlinear Mathematical Physics, 2022
AbstractIn this work, we apply the $$\overline{\partial }$$ ∂ ¯ -dressing method to study the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation (CLL–NLS) with non-normalization boundary conditions.
Sun, Shi-Fei, Li, Biao
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ANALYSIS OF NONLINEAR EQUATIONS IN PRIVATE DERIVATIVES ASSOCIATED WITH THE THIRD-ORDER SCATTERING OPERATOR

Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020
Background. A plurality of nonlinear equations in partial derivatives having a Lax pair are either exactly integrable or equations that allow rich classes of exact solutions.
T. V. Red'kina, O. V. Novikova
doaj   +1 more source

On multi-dimensional partial differential equations with power nonlinearities in first derivatives [PDF]

Ufimskii Matematicheskii Zhurnal, 2017
Summary: We consider a class of multi-dimensional partial differential equations involving a linear differential operator of arbitrary order and a power nonlinearity in the first derivatives. Under some additional assumptions for this operator, we study the solutions of multi-dimensional travelling waves that depend on some linear combinations of the ...
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Numerical solution of the multi-term variable-order space fractional nonlinear partial differential equations [PDF]

, 2021
A numerical approach for solving the multi-term variable-order space fractional nonlinear partial differential equations is proposed. The fractional derivatives are described in the Caputo sense.
Yaslan, H. Cerdik
core   +1 more source

An Initial Problem for a Class of Weakly Degenerate Semilinear Equations with Lower Order Fractional Derivatives

Известия Иркутского государственного университета: Серия "Математика", 2021
An initial value problem is studied for a class of evolutionary equations with a weak degeneration, which are nonlinear with respect to lower order fractional Gerasimov – Caputo derivatives.
G.D. Baybulatova, M.V. Plekhanova
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A note on exp-function method combined with complex transform method applied to fractional differential equations

Advances in Nonlinear Analysis, 2015
In this article, the fractional derivatives in the sense of modified Riemann–Liouville and the exp-function method are used to construct exact solutions for some nonlinear partial fractional differential equations via the nonlinear fractional Liouville ...
Guner Ozkan, Bekir Ahmet, Bilgil Halis
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Fractional Reduced Differential Transform Method for Solving Mutualism Model with Fractional Diffusion

International Journal of Analysis and Applications, 2023
This study presents the fractional reduced differential transform method for a nonlinear mutualism model with fractional diffusion. The fractional derivatives are described by Caputo's fractional operator.
Mohamed Ahmed Abdallah, Khaled Abdalla Ishag   +1 more
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Continuity equations and ODE flows with non-smooth velocity [PDF]

, 2014
In this paper we review many aspects of the well-posedness theory for the Cauchy problem for the continuity and transport equations and for the ordinary differential equation (ODE). In this framework, we deal with velocity fields that are not smooth, but
Crippa, Gianluca, Ambrosio, Luigi
core   +1 more source