solitary wave solutions for compound kdv type and compound kdv burgers type equations with nonlinear terms of any order in this letter based on the idea of adomian s decomposition method and with help of mathematica we obtain the exact solutions for compound kdv type and compound kdv burgers type equations with nonlinear terms of any order in this paper by considering the decomposition scheme we first obtain the exact solutions of these two equation for the initial conditions without using any classical transformations and then their numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions their remarkable accuracy is finally demonstrated in the study of some values p 1 of the compound kdv type and compound kdv burgers type equations

stable sequential identification of continuous nonlinear dynamical systems by growing radial basis function networks this paper presents a sequential identification scheme for continuous nonlinear dynamical systems using neural networks the nonlinearities of the dynamical systems are assumed to be unknown the identification model is a gaussian radial basis function neural network that grows gradually to span the appropriate state space and of sufficient complexity to provide an approximation to the dynamical system the sequential identification algorithm for continuous dynamical nonlinear systems is developed in the continuous time framework instead of in discrete time the approach different from the conventional methods of optimizing a cost function attempts to ensure stability of the overall system while the neural network learns the system dynamics the stability and convergence of the overall identification scheme are guaranteed by parameter adjustment laws developed using the lyapunov synthesis approach to ensure that the modelling error can be reduced arbitrarily a one to one mapping is proposed so that th

solitary wave and periodic wave solutions for the thermally forced gravity waves in atmosphere by introducing a new transformation a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system which extends fan s direct algebraic method to the case when r 4 the solutions of a first order nonlinear ordinary differential equation with a higher degree nonlinear term and fan s direct algebraic method of obtaining exact solutions to nonlinear partial differential equations are applied to the combined kdv mkdv gkdv equation which is derived from a simple incompressible non hydrostatic boussinesq equation with the influence of thermal forcing and is applied to investigate internal gravity waves in the atmosphere as a result by taking advantage of the new first order nonlinear ordinary differential equation with a fifth degree nonlinear term and an eighth degree nonlinear term periodic wave solutions associated with the jacobin elliptic function and the bell and kink profile solitary wave solutions are obtained under the effect of thermal forcing most importantly the mechanism of propagation and generation of the periodic waves and the solitary waves is analysed in detail according to the values of the heating parameter which show that the effect of heating in atmosphere helps to excite westerly or easterly propagating periodic internal gravity waves and internal solitary waves in atmosphere which are affected by the local excitation structures in atmosphere in addition as an illustrative sample the properties of the solitary wave solution and jacobin periodic solution are shown by some figures under the consideration of heating interaction

backlund transformations and solutions to kdv type equations backlund transformations for the non potential mkdv equation and its calogero degasperis fokas modifications are presented and used for finding particular wave type solutions to the equations

exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method the authors present a systematic and formal approach toward finding solitary wave solutions of nonlinear evolution and wave equations from the real exponential solutions of the underlying linear equations the physical concept is one of the mixing of these elementary solutions through the nonlinearities in the system the emphasis is however on the mathematical aspects i e the formal procedure necessary to find single solitary wave solutions by means of examples it is shown how various cases of pulse type and kink type solutions are to be obtained by this method an exhaustive list of equations so treated is presented in tabular form together with the particular intermediate relations necessary for deriving their solutions the extension of the technique to construct n soliton solutions and indicate connections with other existing methods is outlined

explicit exact solutions for new general two dimensional kdv type and two dimensional kdv burgers type equations with nonlinear terms of any order in this paper we have improved the tanh method by means of a proper transformation and a general ansatz applying the improved method and direct assumption method with symbolic computation we consider two kinds of equations general two dimensional kdv type equations with nonlinear terms

double basis multiplicative inversion over gf 2 sup m inversion over galois fields is much more difficult than the corresponding multiplication efficient computation of inverses in gf 2 sup m is considered by solving a set of linear equations over the ground field gf 2 the proposed algorithm uses two separate bases for the representation of its input and output elements and has low computational complexity the algorithm is also suitable for hardware implementation using vlsi technologies

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

on series expansions giving closed form solutions of korteweg de vries like equations korteweg devries kdv like equations with higher degree nonlinearity are solved by a direct algebraic technique due to hereman et al j phys a 19 1986 pp 607 628 for two kdv like equations one with fifth degree nonlinearity the other a combined kdv and mkdv equation for particular choices of the coefficients of the nonlinear terms the kink and antikink solutions found by dey are recovered furthermore soliton solutions of the combined kdv and mkdv equation are found for all values of the coefficients closed form solutions for the calogero degasperis fokas modified mkdv equation are also developed applications of the solutions of these equations in quantum field theory plasma physics and solid state physics are mentioned the hereman et al method is illustrated and slightly extended and this direct series method is briefly compared to hirota s method

solitary wave solutions of nonlinear evolution and wave equations using a direct method and macsyma the direct algebraic method for constructing travelling wave solutions on nonlinear evolution and wave equations has been generalized and systematized the class of solitary wave solutions is extended to analytic rather than rational functions of the real exponential solutions of the linearized equation expanding the solutions in an infinite series in these real exponentials an exact solution of the nonlinear pde is obtained whenever the series can be summed methods for solving the nonlinear recursion relation for the coefficients of the series and for summing the series in closed form are discussed the algorithm is now suited to solving nonlinear equations by any symbolic manipulation program this direct method is illustrated by constructing exact solutions of a generalized kdv equation the kuramoto sivashinski equation and a generalized fisher equation

some new and general solutions to the compound kdv burgers system with nonlinear terms of any order abstract in this letter a new riccati equation expansion method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations the main idea of this method is to take full advantage of the solutions of the riccati equation to construct exact travelling wave solutions of nonlinear partial differential equations as a result some more generalized solutions which contain triangular periodic solutions exp function solutions and the soliton like solutions are obtained

domain wall solutions of kdv like equations with higher order nonlinearity the author considers certain nonlinear partial differential equations which are korteweg de vries kdv like equations with higher order nonlinearity it is shown that these have kink domain wall solutions for particular values of the coefficients of the nonlinear terms the solutions are compared with the standard known solution of the lambda phi 2n field theories some conservation laws for these systems of equations are also given

indirect techniques for adaptive input output linearization of non linear systems abstract a technique of indirect adaptive control based on certainty equivalence for input output linearization of non linear systems is proven convergent it does not surfer from the overparameterization drawbacks of the direct adaptive control techniques on the same plant this paper also contains a semi indirect adaptive controller which has several attractive features of both the direct and indirect schemes

exp function method for the exact solutions of fifth order kdv equation and modified burgers equation abstract in this paper we implemented the exp function method for the exact solutions of the fifth order kdv equation and modified burgers equation by using this scheme we found some exact solutions of the above mentioned equations

on the integrability of schamel s modified korteweg de vries dequation a recent suggestion of integrability of schamel s 1973 modified korteweg de vries equation for ion acoustic waves in a two component plasma is discussed various arguments including ones based on the truncated painleve expansion are presented which support the existence of special structure for this equation however the evidence for complete integrability of schamel s equation is not yet conclusive

reduction technique for matrix nonlinear evolution equations solvable by the spectral transform the main purpose of this paper is to describe a technique of reduction whereby from the class of evolution equations for matrices of order n solvable via the spectral transform associated to the matrix linear schrodinger eigenvalue problem one derives subclasses of nonlinear evolution equations involving less than n2 fields to illustrate the method from the equations for matrices of order 2 two subclasses of equations for 2 fields rather than 4 are obtained the first class coincides or rather includes that solvable via the spectral transform associated to the generalized zakharov shabat spectral problem further reduction to nonlinear evolution equations for a single field reproduces a number of well known equations but also yields a novel one highly nonlinear the second class also yields highly nonlinear equations some examples are given including another novel evolution equation for a single field

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

dynamic structure neural networks for stable adaptive control of nonlinear systems an adaptive control technique using dynamic structure gaussian radial basis function neural networks that grow in time according to the location of the system s state in space is presented for the affine class of nonlinear systems having unknown or partially known dynamics the method results in a network that is economic in terms of network size for cases where the state spans only a small subset of state space by utilizing less basis functions than would have been the case if basis functions were centered on discrete locations covering the whole relevant region of state space additionally the system is augmented with sliding control so as to ensure global stability if and when the state moves outside the region of state space spanned by the basis functions and to ensure robustness to disturbances that arise due to the network inherent approximation errors and to the fact that for limiting the network size a minimal number of basis functions are actually being used adaptation laws and sliding control gains that ensure system stability in a lyapunov sense are presented together with techniques for determining which basis functions are to form part of the network structure the effectiveness of the method is demonstrated by experiment simulations

a new general algebraic method with symbolic computation and its application to two nonlinear differential equations with nonlinear terms of any order in this paper with the help of symbolic computation system maple we present a new generalized riccati equation rational expansion method and successfully obtain some new rational formal solutions of some nonlinear partial differential equation with nonlinear terms of any order the presented method can also be applied to other nonlinear evolution equations with nonlinear terms of any order

traveling waves to a burgers korteweg de vries type equation with higher order nonlinearities abstract in this paper first we survey some recent advances in the study of traveling wave solutions to the burgers korteweg de vries equation and some comments are given then we study a burgers korteweg de vries type equation with higher order nonlinearities a qualitative analysis to a two dimensional autonomous system which is equivalent to the burgers kdv type equation is presented and indicates that under certain conditions the burgers korteweg de vries type equation has neither nontrivial bell profile solitary waves nor periodic waves finally a solitary wave solution is obtained by means of the first integral method which is based on the ring theory of commutative algebra