the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

multiple internal layer solutions generated by spatially oscillatory perturbations abstract for a singularly perturbed system of reaction diffusion equations we study the bifurcation of internal layer solutions due to the addition of a spatially oscillatory term in the singular limit the existence and stability of internal layer solutions are determined by the intersection of a fast jump surface 1 and a slow switching curve c the case when the intersection is transverse was studied by x b lin construction and asymptotic stability of structurally stable internal layer solutions preprint in this paper we show that when 1 intersects with c tangentially saddle node or cusp type bifurcation may occur higher order expansions of internal layer solutions and eigenvalue eigenfunctions are also presented to find a true internal layer solution and true eigenvalue eigenfunctions we use a newton s method in functions spaces that is suitable for numerical computations

electromagnetic scattering from general bi isotropic objects using time domain integral equations combined with pmchwt formulations electromagnetic scattering by general bi isotropic objects is calculated by using the time domain integral equations which are incorporated with the poggio miller chang harrington wu tsai pmchwt formulations by introducing a pair of equivalent electric and magnetic sources electromagnetic fields inside a homogeneous bi isotropic region can be represented by these sources over its boundary after applying fields splitting method a series of coupled surface integral equations are obtained after imposing boundary conditions these equations are then solved numerically using the method of moment mom which involves separate spatial and temporal testing procedures the rao wilton glisson rwg functions are used as the spatial expansion and testing functions and the weighted laguerre functions are derived as the temporal basis and testing functions numerical results such as transient currents far scattered fields and normalized radar cross sections are presented and compared with analytical results as well as mom based frequency domain analysis and good agreements are observed

painleve expansions for nonintegrable evolution equations abstract the wtc method is applied to a variety of nonintegrable nonlinear evolution equations and shown to provide a systematic procedure for obtaining special solutions some of the special techniques developed for integrable systems are also shown to be applicable to nonintegrable equations

time domain finite difference and finite element methods for maxwell equations in complex media extensions of finite difference time domain fdtd and finite element time domain fetd algorithms are reviewed for solving transient maxwell equations in complex media also provided are a few representative examples to illustrate the modeling capabilities of fdtd and fetd for complex media the term complex media refers here to media with dispersive bi anisotropic inhomogeneous and or nonlinear properties present in the constitutive tensors

heteroclinic bifurcation and singularly perturbed boundary value problems abstract we study a singularly perturbed boundary value problem in r m n x f x y e e y g x y e b 1 x 0 y 0 e 0 b 2 x 0 y 0 e 0 given a candidate for the 0th order approximation which exhibits both boundary layers and interior layers we present a complete procedure to compute higher order expansions and a procedure to compute the real solution near a truncated asymptotic expansion assuming the hyperbolicity of the regular layers and some generic assumptions similar results concerning the existence of periodic solutions relaxation oscillations are also presented several ideas from dynamical systems theory are employed e g exponential dichotomies fredholm alternatives and heteroclinic bifurcations

painleve analysis and integrability properties of a 2 1 nonrelativistic field theory a model for planar phenomena introduced by jackiw and pi and described by a lagrangian including a chern simons term is considered the associated equations of motion among which there is a 2 1 gauged nonlinear schrodinger equation are rewritten into a gauge independent form involving the modulus of the matter field application of a painleve analysis as adapted to partial differential equations by weiss tabor and carnevale shows up resonance values that are all integer however compatibility conditions need be considered which cannot be satisfied consistently in general such a result suggests that the examined equations are not integrable but provides tools for the investigation of the integrability of different reductions this in particular puts forward the familiar integrable liouville and 1 1 nonlinear schrodinger equations

bi fdtd a novel finite difference time domain formulation for modeling wave propagation in bi isotropic media this paper presents a newly developed finite difference time domain fdtd technique referred to as bi fdtd for modeling electromagnetic wave interactions with bi isotropic bi media the theoretical foundation for the bi fdtd method will be developed based on a wavefield decomposition the main advantage of this approach is that the two sets of wavefields are uncoupled and can be viewed as propagating in an equivalent isotropic medium which makes it possible to readily apply conventional fdtd analysis techniques the bi fdtd scheme will also be extended to include the dispersive nature of chiral media an important subclass of bi isotropic media this extension represents the first of its kind in the fdtd community validations of this new model are demonstrated for a chiral half space and a chiral slab

tracking invariant manifolds with differential forms in singularly perturbed systems abstract a technique is developed for finding homoclinic orbits in singularly perturbed systems the desired orbit lies near a singular solution that has both fast and slow time scales the orbit is to be constructed as the transverse intersection of a center stable and center unstable manifold which requires tracking the invariant manifolds near the singular solution the main technical advance is the exchange lemma which allows one to convert information about transversality of manifolds associated with the singular limit equations to information about behavior of the invariant manifold as it leaves a neighborhood of a slow segment of the singular solution the computations for this lemma are done with the use of differential forms and the lemma is applied to prove the existence of a homoclinic orbit in a class of singularly perturbed equations

link between solitary waves and projective riccati equations many solitary wave solutions of nonlinear partial differential equations can be written as a polynomial in two elementary functions which satisfy a projective hence linearizable riccati system from that property the authors deduce a method for building these solutions by determining only a finite number of coefficients this method is much shorter and obtains more solutions than the one which consists of summing a perturbation series built from exponential solutions of the linearized equation they handle several examples for the henon heiles hamiltonian system they obtain several exact solutions one of them defines a new solitary wave solution for a coupled system of boussinesq and nonlinear schrodinger equations for a third order dispersive equation with two monomial nonlinearities they isolate all cases where the general solution is single valued

modelling of wave propagation in wire media using spatially dispersive finite difference time domain method numerical aspects the finite difference time domain fdtd method is applied for modelling of wire media as artificial dielectrics both frequency dispersion and spatial dispersion effects in wire media are taken into account using the auxiliary differential equation method according to the authors knowledge this is the first time when the spatial dispersion effect is considered in the fdtd modelling the stability of developed spatially dispersive fdtd formulations is analyzed through the use of von neumann method combined with the routh hurwitz criterion the results show that the conventional stability courant limit is preserved using standard discretization scheme for wire media modelling flat sub wavelength lenses formed by wire media are chosen for validation of proposed spatially dispersive fdtd formulation results of the simulations demonstrate excellent sub wavelength imaging capability of the wire medium slabs the size of the simulation domain is significantly reduced using the modified perfectly matched layer mpml which can be placed in close vicinity of the wire medium it is demonstrated that the reflections from the mpml wire medium interface are less than 70 db that lead to dramatic improvement of convergence compared to conventional simulations

on the integrability of systems of nonlinear ordinary differential equations with superposition principles a new class of solvable nonlinear dynamical systems has been recently identified by the requirement that the ordinary differential equations ode s describing each member of this class possess nonlinear superposition principles these systems of ode s are generally not derived from a hamiltonian and are classified by associated pairs of lie algebras of vector fields in this paper all such systems of n 3 ode s are integrated in a unified way by finding explicit integrals for them and relating them all to a pivotal member of their class the projective riccati equations moreover by perturbing two parametrically driven projective riccati equations thus making them nonsolvable in the above sense evidence is discovered of chaotic behavior on the poincare surface of section in the form of sensitive dependence on initial conditions near a boundary separating bounded from unbounded motion

fast and slow waves in the fitzhugh nagumo equation abstract it is known that the fitzhugh nagumo equation possesses fast and slow travelling waves fast waves are perturbations of singular orbits consisting of two pieces of slow manifolds and connections between them whereas slow waves are perturbations of homoclinic orbits of the unperturbed system we unfold a degenerate point where the two types of singular orbits coalesce forming a heteroclinic orbit of the unperturbed system let c denote the wave speed and e the singular perturbation parameter we show that there exists a c 2 smooth curve of homoclinic orbits of the form c e c connecting the fast wave branch to the slow wave branch additionally we show that this curve has a unique non degenerate maximum our analysis is based on a shilnikov coordinates result extending the exchange lemma of jones and kopell we also prove the existence of inclination flip points for the travelling wave equation thus providing the evidence of the existence of n homoclinic orbits n pulses for the fitzhugh nagumo equation for arbitrary n

mixed function method for obtaining exact solution of nonlinear differential difference equations and coupled nddes in this paper we construct a new mixed function method for the first time by using this new method we study the two nonlinear differential difference equations named the generalized hybrid lattice and two component volterra lattice equations some new exact solutions of mixed function type such as discrete solitary wave solutions discrete kink and anti kink wave solutions and discrete breather solutions with kink and anti kink character are obtained and their dynamic properties are also discussed by using software mathematica we show their profiles

the painleve property for partial differential equations ii backlund transformation lax pairs and the schwarzian derivative in this paper we investigate the painleve property for partial differential equations by application to several well known partial differential equations burgers kdv mkdv bousinesq higher order kdv and kp equations it is shown that consideration of the singular manifold leads to a formulation of these equations in terms of the schwarzian derivative this formulation is invariant under the moebius group acting on dependent variables and is shown to obtain the appropriate lax pair linearization for the underlying nonlinear pde

the conserved quantities and symmetries of the two dimensional toda lattice hierarchy the conserved quantities and symmetries of the soliton equations included in the 2dtl two dimensional toda lattice hierarchy are considered by means of the theory of the function a typical example is presented for the 2dtl equation that is the simplest nontrivial equation in the hierarchy then by applying suitable reductions the cases of the toda lattice equation and the sine gordon equation are discussed

adomian decomposition and pade approximate for solving differential difference equation abstract in this paper we apply the adomian decomposition method and pade approximate to solving the differential difference equations ddes for the first time a simple but typical example is used to illustrate the validity and the great potential of the adomian decomposition method adm in solving ddes comparisons are made between the results of the proposed method and exact solutions the results show that adm is an attractive method in solving the differential difference equations

shadowing lemma and singularly perturbed boundary value problems a complete procedure is given to determine the outer and inner expansions of a singularly perturbed boundary value problem in mathbb r n the validity of such expansions is deduced from a gene

a symbolic computational method for constructing exact solutions to difference differential equations in this paper we extended tanh method to solve difference differential equations and pure difference equations with the projective riccati equation as an example we applied this method to a 2 1 dimensional toda lattice equation as a result many exact solutions are obtained with the help of symbolic system maple including soliton solutions presented by hyperbolic functions sinh and cosh periodic solutions presented by sin and cos and rational solutions this method can also be used to other nonlinear difference differential equations

transversal heteroclinic and homoclinic orbits in singular perturbation problems abstract in this paper we give a geometric construction of heteroclinic and homoclinic orbits for singularly perturbed differential equations by using methods from invariant manifold theory we show that transversal intersection of stable and unstable manifolds of the reduced problem implies the existence of transversal heteroclinic or homoclinic orbits of the singularly perturbed problem we derive analytical conditions for transversality we show how these results can be used to prove the existence of heteroclinic and homoclinic orbits in singularly perturbed problems which depend on additional parameters we describe a configuration which implies transversal intersection of the stable and unstable manifolds of periodic orbits and the associated chaotic dynamics

on the complete and partial integrability of non hamiltonian systems abstract the methods of singularity analysis are applied to several third order non hamiltonian systems of physical significance including the lotka volterra equations the three wave interaction and the rikitake dynamo model complete integrability is defined and new completely integrable systems are discovered by means of the painleve property in all these cases we obtain integrals which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation ode solved by painleve transcendents relaxing the painleve property we find many partially integrable cases whose movable singularities are poles at leading order with in t t 0 terms entering at higher orders in an n th order generalized rossler model a precise relation is established between the partial fulfillment of the painleve conditions and the existence of n 2 integrals of the motion

generalizing homotopy analysis method to solve lotka volterra equation in the paper we generalized the homotopy analysis method to solve lotka volterra equation as a simple but typical example it illustrates the validity and the great potential of the homotopy analysis method to solve differential difference equations comparisons are made between the results of the proposed method and exact solutions the results reveal that the proposed method is valid for the lotka volterra equation

a family of completely integrable multi hamiltonian systems explicitly related to some celebrated equations by introducing a spectral problem with an arbitrary parameter we derive a kaup newell type hierarchy of nonlinear evolution equations which is explicitly related to many important equations such as the kundu equation the kaup newell kn equation the chen lee liu cll equation the gerdjikov ivanov gi equation the burgers equation the modified korteweg devries mkdv equation and the sharma tasso olver equation it is shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure under the bargann constraint between the potentials and the eigenfunctions the spectral problem is nonlinearized as a finite dimensional completely integrable hamiltonian system the involutive representation of the solutions for the kaup newell type hierarchy is also presented in addition an n fold darboux transformation of the kundu equation is constructed with the help of its lax pairs and a reduction technique according to the darboux transformation the solutions of the ku