In this paper, reduced differential transform method (RDTM) is employed to
approximate the solutions of (2+1) dimensional type of the Zakharov-Kuznetsov
partial differential equations. We apply these method to two examples. Thus, we
have obtained numerical solution partial differential equations of
Zakharov-Kuznetsov. These examples are prepared to show the efficiency and
simplicity of the method

Acan, Omer

Keskin, Yildiray

arXiv.org e-Print Archive

Crossref

English

Reduced Differential Transform Method for (2+1) Dimensional type of the
  Zakharov-Kuznetsov ZK(n,n) Equations

Pejsachowicz, Jacobo

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

PORTO Publications Open Repository TOrino

A global index for bifurcation of ﬁxed points,

A periodicity theorem in the algebra of symbols,

A simple notion of orientability for Fredholm maps of index zero between Banach manifolds and degree,

Algebraic Topology – Homotopy and Homology,

Analytic theory of global bifurcation. An introduction,

and generalized multiplicity,

Applied equivariant degree,

Bifurcation of extremals of Fredholm functionals,

Bifurcation of Fredholm maps II; The dimension of the bifurcation set, in preparation.

Bifurcation of homoclinics,

Bifurcation of zeroes of parametrized functions,

Bifurcation theory for Fredholm operators,

bifurcation, Topological Nonlinear Analysis,

Boundary Problems, Partial Diﬀerential Equations IX, Encyclopedia of Mathematical Sciences,

Boundary Value Problems for Elliptic Systems,

Calculating bifurcation invariants as elements in the homotopy of the general linear group,

Characteristic Classes,

complexes,

Degree theory for C1-Fredholm mappings of index 0,

Diﬀerential and Riemannian Manifolds,

Diﬀerential forms in algebraic topology,

Eigenvalue inequalities for fermions in gauge theories,

Elliptic singular integro-diﬀerential operators,

Equivariant Degree Theory,

Estimates near the boundary for solutions of elliptic partial diﬀerential equations satisfying general boundary conditions II,

Fiberwise Homotopy Theory,

Fibre Bundles,

Foundations of Global Nonlinear Analysis,

Fundamental group of the space of Fredholm operators and global analysis of non linear equations,

Global bifurcation of quasilinear elliptic equations on RN,

Global several parameter bifurcation and continuation theorems,

Group theoretic methods in bifurcation theory,

Harmonic spinors,

Homotopy, linearization, and bifurcation,

Index theorems, Partial Diﬀerential Equations VIII,

Index Theory of Elliptic Boundary Problems, North Oxford Academic,

Inﬁnite dimensional K-theory and characteristic classes of Fredholm bundle maps,

Integro-diﬀerential operators on vector bundles,

Introduction ` a la Th´ eorie des ´ Equations aux D´ eriv´ ees Partielles Lin´ eaires, Gauthier–Villars,

K-theoretic methods in bifurcation theory,

Lectures on Topics in One-Parameter Bifurcation Problems, Tata Inst.

Methods of bifurcation theory,

Morse Theory,

Multiple eigenvalue bifurcation for Fredholm mappings,

Nonlinear Fredholm maps and Leray–Schauder theory,

of the index bundle and several-parameter bifurcation,

On oriented degree of a certain class of perturbations of Fredholm mappings and on bifurcations of solutions of a nonlinear boundary value problem with noncompact perturbations,

On the Adams conjecture,

On the groups J(X) I,

Oriented degree of Fredholm maps of nonnegative index and its application to global bifurcation of solutions, Global Analysis Studies and Applications V,

periodicity and the index of elliptic operators,

Sulle corrispondenze funzionali inverse diramate: teoria generale e applicazioni ad alcune equazioni funzionali nonlineari e al problema di Plateau,

The degree for proper C2 Fredholm mappings I,

The global structure of the zero set of a family of semilinear Fredholm maps,

The index of an elliptic system on a manifold,

The index of elliptic operators

The index of elliptic operators IV,

The Leray–Schauder reduction and bifurcation for parametrized families of nonlinear elliptic boundary value problems,

Theory of branching of solutions of non-linear equations

theory. An introduction with applications to PDEs,

Topological invariants of bifurcation, C∗-algebras and elliptic theory II, Trends Math.

Topology and Analysis,

Vektorraumb¨ undel und der Raum der Fredholm-Operatoren,

Bifurcation of Fredholm maps I; Index bundle and bifurcation

We associate to a parametrized family $f$ of nonlinear Fredholm maps
possessing a trivial branch of zeroes an {\it index of bifurcation} $\beta(f)$
which provides an algebraic measure for the number of bifurcation points from
the trivial branch. The index $\beta(f)$ is derived from the index bundle of
the linearization of the family along the trivial branch by means of the
generalized $J$-homomorphism. Using the Agranovich reduction and a
cohomological form of the Atiyah-Singer family index theorem, due to Fedosov,
we compute the bifurcation index of a multiparameter family of nonlinear
elliptic boundary value problems from the principal symbol of the linearization
along the trivial branch. In this way we obtain criteria for bifurcation of
solutions of nonlinear elliptic equations which cannot be achieved using the
classical Lyapunov-Schmidt method.Comment: 42 pages. Changes: added Lemma 2.31 and a reference + minor
  corrections. To appear on TMN

Akademicka Platforma Czasopism

Bifurcation of Fredholm Maps I; The Index Bundle and Bifurcation