Current Issue : July - September Volume : 2018 Issue Number : 3 Articles : 6 Articles
We constructmetric connection associated with a first-order differential equation bymeans of the generator set of a Pfaffian system\non a submanifold of an appropriate first-order jet bundle.We firstly show that the inviscid and viscous Burgers� equations describe\nsurfaces attached to an ODE of the form...
In this work, we prove that the integrating factors can be used as a reduction method.\nAnalytical solutions of the Jaulentââ?¬â??Miodek (JM) equation are obtained using integrating factors as\nan extension of a recent work where, through hidden symmetries, the JM was reduced to ordinary\ndifferential equations (ODEs). Some of these ODEs had no quadrature. We here derive several new\nsolutions for these non-solvable ODEs....
Generalized matrix exponential solutions to the AKNS equation are obtained by the inverse scattering transformation (IST). The\nresulting solutions involve six matrices, which satisfy the coupled Sylvester equations. Several kinds of explicit solutions including\nsoliton, complexiton, and Matveev solutions are deduced from the generalized matrix exponential solutions by choosing different\nkinds of the six involved matrices. Generalized matrix exponential solutions to a general integrable equation of the AKNS hierarchy\nare also derived. It is shown that the general equation and its matrix exponential solutions share the same linear structure....
Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic\nidentities satisfied by the zeros of a wide class of orthogonal polynomials is derived.The generalization is based on amodification of\npseudospectral matrix representations of linear differential operators proposed in the paper, which allows these representations to\ndepend on two, rather than one, sets of interpolation nodes. The identities hold for every polynomial family {...
One of the most important biochemical reactions is catalyzed by enzymes. A numerical\nmethod to solve nonlinear equations of enzyme kinetics, known as the Michaelis and Menten\nequations, together with fuzzy initial values is introduced. The numerical method is based on the\nfourth order Rungeââ?¬â??Kutta method, which is generalized for a fuzzy system of differential equations.\nThe convergence and stability of the method are also presented. The capability of the method in\nfuzzy enzyme kinetics is demonstrated by some numerical examples....
We focus on the following elliptic system with critical Sobolev exponents: âË?â??div(|âË?â?¡...
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