Results 11 to 20 of about 4,649,717 (295)

Remarks on Nonlinear Evolution Equations

Journal of Mathematical Analysis and Applications, 1996
In the paper fully nonlinear evolution equations \[ {du \over dt} +A(t,u,u) = 0, \quad 0\leq t\leq T,\quad u(0) =\varphi, \] in a Banach space \(X\) are considered. Here \(T>0\), \(A\) is a nonlinear mapping of a subset \(D(A) \subset [0,T] \times X \times X\) into \(X\) and \(\varphi \in X\).
Zhao, Jiabin
openaire   +3 more sources

Potentialisations of a class of fully-nonlinear symmetry-integrable evolution equations [PDF]

Open Communications in Nonlinear Mathematical Physics
We consider here the class of fully-nonlinear symmetry-integrable third-order evolution equations in 1+1 dimensions that were proposed recently in the journal Open Communications in Nonlinear Mathematical Physics, vol. 2, 216--228 (2022).
Marianna Euler, Norbert Euler
doaj   +3 more sources

Observations on the basic (G′/G)-expansion method for finding solutions to nonlinear evolution equations [PDF]

, 2010
The extended tanh-function expansion method for finding solutions to nonlinear evolution equations delivers solutions in a straightforward manner and in a neat and helpful form.
Parkes, E.J.
core   +4 more sources

Finding exact solutions for selected nonlinear evolution differential equations [PDF]

, 2023
Burgers, Breaking Soliton and Boussinesq equations are applicable in different areas of physics. Searching their real solutions are particularly important.
Mohammed, Mayada G.., Strunin, Dmitry V., Bhanot, Rajeev P.   +2 more
core   +1 more source

Observations on the tanh-coth expansion method for finding solutions to nonlinear evolution equations [PDF]

, 2010
The 'tanh-coth expansion method' for finding solitary travelling-wave solutions to nonlinear evolution equations has been used extensively in the literature. It is a natural extension to the basic tanh-function expansion method which was developed in the
Parkes, E.J.
core   +3 more sources

Optimal control of stochastic partial differential equations in Banach spaces [PDF]

, 2010
In this thesis we study optimal control problems in Banach spaces for stochastic partial differential equations. We investigate two different approaches.
Serrano Perdomo, Rafael Antonio
core   +5 more sources

On differential equations invariant under a projective transformation group: integrability and reductions [PDF]

Open Communications in Nonlinear Mathematical Physics
We consider a projective transformation and establish the invariants for this transformation group up to order seven. We use the obtained invariants to construct a class of nonlinear evolution equations and identify some symmetry-integrable equations in ...
Marianna Euler, Norbert Euler, Francesco Oliveri   +2 more
doaj   +1 more source

New exact solutions for time-fractional Kaup-Kupershmidt equation using improved (G′/G)-expansion and extended (G′/G)-expansion methods

Alexandria Engineering Journal, 2020
The mathematical modeling of physical systems is generally governed by evolution equations in nonlinear form. Therefore, it is critical to obtain exact analytical solutions to these equations.
S. Sahoo, S. Saha Ray, M.A. Abdou
doaj   +1 more source

Representation of exact solutions of ψ-fractional nonlinear evolution equations using two different approaches

Partial Differential Equations in Applied Mathematics, 2021
In this paper, we investigate the applicability of the separation of variables method (SVM) and the invariant subspace method (ISM) for getting exact solutions of variable coefficients nonlinear fractional partial differential equations with ψ-Riemann ...
Abass. H. Abdel Kader, Mohamed S. Abdel Latif, Dumitru Baleanu   +2 more
doaj   +1 more source

Assorted soliton structures of solutions for fractional nonlinear Schrodinger types evolution equations

Journal of Ocean Engineering and Science, 2022
Fractional order nonlinear evolution equations have emerged in recent times as being very important model for depicting the interior behavior of nonlinear phenomena that exist in the real world.
Md. Tarikul Islam, Md. Ali Akbar, J.F. Gómez-Aguilar, E. Bonyah, G. Fernandez-Anaya   +4 more
doaj   +1 more source