a further extended tanh function method and new soliton like solutions to the integrable broer kaup bk equations in 2 1 dimensional spaces based on an extended tanh function method a further extended tanh function method is suggested to obtain multiple exact solutions for nonlinear partial differential equations which including soliton like solutions solitary waves and trigonometric function solutions the validity and reliability of the method is tested by its application to the integrable broer kaup equations in 2 1 dimensional spaces more new explicit exact solutions are found

new exact solutions of the broer kaup equations in 2 1 dimensional spaces abstract with the aid of maple several new kinds of exact solutions for the broer kaup equations in 2 1 dimensional spaces are obtained by using a new ansatz this approach can also be applied to other nonlinear evolution equations

explicit solution of a stochastic irreversible investment problem and its moving threshold we consider a firm producing a single consumption good that makes irreversible investments to expand its production capacity the firm aims to maximize its expected total discounted real profit net of investment on a finite horizont the capacity is modeled as a controlled ita process where the control is the real investment which is not necessarily a rate but more generally a monotone process the result is a singular stochastic control problem we introduce the associated optimal stopping problem that is the optimal cost of not investing its variational formulation turns out to be a parabolic obstacle problem which we explicitly solve in the case of constant relative risk aversion crra production functions the moving free boundary is the threshold at which the shadow value of installed capital exceeds the capital s replacement cost then we use the equation of the free boundary to evaluate the optimal investment policy and its corresponding optimal profits

backlund transformation in bilinear form for a higher order nonlinear schrodinger equation backlund transformation in bilinear form is presented for a higher order nonlinear schrodinger equation which describes the propagation of ultrashort light pulses in optical fibers with symbolic computation and starting from the backlund transformation the analytical soliton solution is obtained from a trivial solution and the inverse scattering transform scheme is also derived furthermore the n soliton solution in double wronskian form is given and the value of the arbitrary constant appearing in the backlund transformation is determined for a transformation between the n 1 and n soliton solutions the results obtained from the backlund transformation might be valuable in optical communications

backlund transformation and soliton interactions for the zakharov kuznetsov equation in plasmas abstract symbolically investigated in this paper is the zakharov kuznetsov equation which describes the propagation of the electrostatic excitations in a magnetized rotating and collisionless three component plasma bilinear form and backlund transformation for the zakharov kuznetsov equation are derived with the hirota method and symbolic computation n soliton solutions in terms of the wronskian determinant are constructed and the verification is finished through the direct substitution into bilinear equations propagation characteristics and interaction behaviors of the solitons are discussed through a graphical analysis during the propagation the one soliton width and amplitude are both unchanged and not related to the coefficients while the soliton interactions are elastic

infinite dimensional linear programming approach to singularstochastic control we consider a multidimensional singular stochastic control problem with state dependent diffusion matrix and drift vector and control cost depending on the position and direction of displacement of the controlled process the objective is to minimize the total expected discounted cost we write an equivalent infinite dimensional linear programming problem on a subspace of the space conjugate to cal c bbb r n times cal c bbb r n times b where b is the unit sphere in bbb r n we write a dual linear program and prove absence of duality gap the dual program characterizes the optimal cost function as a maximal solution to the variational inequality with gradient constraints

singular optimal stochastic controls ii dynamic programming the dynamic programming principle for a multidimensional singular stochastic control problem is established in this paper when assuming lipschitz continuity on the data it is shown that the value function is continuous and is the unique viscosity solution of the corresponding hamilton jacobi bellman equation

singular stochastic control linear diffusions and optimal stopping a class of solvable problems we consider a class of singular stochastic control problems arising frequently in applications of stochastic control we state a set of conditions under which the optimal policy and its value can be derived in terms of the minimal r excessive functions of the controlled diffusion and demonstrate that the optimal policy is of the standard local time type we then state a set of weak smoothness conditions under which the value function is increasing and concave and demonstrate that given these conditions increased stochastic fluctuations decrease the value and increase the optimal threshold thus postponing the exercise of the irreversible policy in line with previous studies of singular stochastic control we also establish a connection between singular control and optimal stopping and show that the marginal value of the singular control problem coincides with the value of the associated stopping problem whenever 0 is not a regular boundary for the controlled diffusion

symbolic computation on the darboux transformation for a generalized variable coefficient higher order nonlinear schrodinger equation from fiber optics considering the propagation of ultrashort pulse in the realistic fiber optics a generalized variable coefficient higher order nonlinear schrodinger equation is investigated in this paper under certain constraints a new 3 3 lax pair for this equation is obtained through the ablowitz kaup newell segur procedure furthermore with symbolic computation the darboux transformation and nth iterated potential transformation formula for such a model are explicitly derived the corresponding features of ultrashort pulse in inhomogeneous optical fibers are graphically discussed by the one and two soliton like solutions

brownian motion in a wedge with variable reflection existence and uniqueness existence and uniqueness in law of reflecting brownian motion in a wedge is proved the direction of reflection along the sides of the wedge varies in a reasonable fashion except perhaps at the corner

a skorohod type lemma and a decomposition of reflected brownian motion we consider two dimensional reflected brownian motions in sharp thorns pointed downward with horizontal vectors of reflection we present a decomposition of the process into a brownian motion and a process which has bounded variation away from the tip of the thorn the construction is based on a new skorohod type lemma

darboux transformation and hamiltonian structure for the jaulent miodek hierarchy abstract starting from the jaulent miodek spectral problem we derive the associated hierarchy of nonlinear evolution equations in this paper it is shown that this hierarchy is completely integrable in the liouville sense and possesses the hamiltonian structure moreover by virtue of symbolic computation two types of darboux transformations for the whole hierarchy are explicitly constructed which enables us to find the new soliton like shock and anti shock solutions for the jaulent miodek hierarchy figures are presented to discuss the properties of the new soliton like solutions

soliton solutions and backlund transformation for the normalized linearly coupled nonlinear wave equations with symbolic computation abstract under investigation in this paper are the normalized linearly coupled nonlinear wave equations which can be used to describe the pulse propagation in the two core optical fiber based on the hirota s method and symbolic computation the bilinear form and soliton solutions for the equations are derived furthermore backlund transformation bt in bilinear forms is given through the bt a type of solutions and lax pair are derived under certain conditions propagation characteristics and interaction behaviors of the solitons are discussed through the graphical analysis results of this paper might be helpful for the future development of some optical devices used in the modern optical communication systems such as the directional couplers polarization splitters interferometers and modulators

brownian motion in a wedge with oblique reflection this work is concerned with the existence and uniqueness of a strong markov process that has continuous sample paths and the following additional properties i the state space is an infinite two dimensional wedge and the process behaves in the interior of the wedge like an ordinary brownian motion ii the process reflects instantaneously at the boundary of the wedge the angle of reflection being constant along each side iii the amount of time that the process spends at the comer of the wedge is zero i e the set of times for which the process is at the comer has lebesgue measure zero hereafter let be the angle of the wedge 0 2 let 1 and 2 be the angles of reflection on the two sides of the wedge measured from the inward normals the positive angles being toward the corner 1 2 and set 1 2 the question of existence and uniqueness is recast as a submartingale problem in the style used by stroock and varadhan diffusion processes with boundary conditions comm pure appl math 24 1971 pp 147 225 for diffusions on smooth domains with smooth boundary conditions it is shown that no solution exists if 2 in this case there is a unique continuous strong markov process satisfying i ii above it reaches the corner of the wedge almost surely and it remains there if 2 however then there is a unique continuous strong markov process statisfying i iii it is shown that starting away from the corner this process does not reach the corner of the wedge if 0 and does reach the corner if 0 2 the general theory of multi dimensional diffusions does not apply to the above problem because in general the boundary of the state space is not smooth and there is a discontinuity in the direction of reflection at the corner for some values of the process arises from diffusion approximations to storage systems and queueing networks i the state space is an infinite two dimensional wedge and the process behaves in the interior of the wedge like an ordinary brownian motion ii the process reflects instantaneously at the boundary of the wedge and the angle of reflection being constant along each side iii the amount of time that the process spends at the corner of the wedge is zero i e the set of times for which the process is at the corner has lebesgue measure zero

new families of exact solutions to the integrable dispersive long wave equations in 2 1 dimensional spaces the integrable dispersive long wave equations especially the higher dimensional ones are of current interest in both physics and mathematics obtained in this paper via a symbolic computation based method are new families of exact solutions to the 2 1 dimensional integrable dispersive long wave equations sample solutions from those families are presented solitary waves are merely a special case in one family

the investigation for 2 1 dimensional eckhaus type extension of the dispersive long wave equation the 2 1 dimensional eckhaus type extension of the dispersive long wave eedlw equation is investigated which was obtained in the appropriate approximation from the basic equations of hydrodynamics though it has no painleve property we gain an auto backlund transformation abt by truncating the laurent series expansion at o w0 in particular the special one of the abt establishes a relationship between the eedlw equation and a set of three linear partial differential equations involving the well known heat equation finally many types of new exact solutions of the eedlw equation are found from the obtained abt and some proper ansatze which may be useful to explain some physical phenomena

multi soliton solutions and a backlund transformation for a generalized variable coefficient higher order nonlinear schrodinger equation with symbolic computation abstract in this paper by virtue of symbolic computation the investigation is made on a generalized variable coefficient higher order nonlinear schrodinger equation with varying higher order effects and gain or loss which can describe the femtosecond optical pulse propagation in a monomode dielectric waveguide a modified dependent variable transformation is introduced into the bilinear method to transform such an equation into a variable coefficient bilinear form based on the formal parameter expansion technique the multi soliton solutions of this equation are obtained through the bilinear form under sets of parametric constraints a backlund transformation in bilinear form is also obtained for the first time in this paper finally discussions on the analytic soliton solutions are given and various propagation situations are illustrated

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

types of solutions of the variable coefficient nonlinear schrodinger equation with symbolic computation by using hirota s bilinear method and symbolic computation solutions for a variable coefficient nonlinear schrodinger equation are obtained theoretically it is found that the type of the solutions changes with the different choices of the group velocity dispersion coefficient beta 2 z according to those solutions the relevant properties and features of physical and optical interest are illustrated in addition an effective technique for controlling the shape of the pulses is presented the results of this paper will be valuable to the study of the future development of ultrahigh rate and long distance optical communication systems

darboux transformation and explicit solutions for the integrable sixth order kdv equation for nonlinear waves abstract korteweg de vries kdv type equations can describe some physical phenomena in fluids nonlinear optics quantum mechanics plasmas etc in this paper with the aid of symbolic computation the integrable sixth order kdv equation is investigated darboux transformation dt with an arbitrary parameter is presented explicit solutions are derived with the dt relevant properties are graphically illustrated which might be helpful to understand some physical processes in fluids plasmas optics and quantum mechanics

symbolic computation and observable effect for the 2 1 dimensional symmetric regularized long wave equation from strongly magnetized cold electron plasmas abstract in this paper with the aid of computerized symbolic computation we use the generalized hyperbolic function method to obtain new families of exact analytic solutions for the 2 1 dimensional symmetric regularized long wave equation this equation describes weakly nonlinear ion acoustic and space charge waves in strongly magnetized cold electron plasmas the families we obtain consist of solitary waves and trigonometric functions we outline an observable 2 1 dimensional effect that could be of interest to future experiments on space and laboratory plasma systems the usage of the wu elimination method has also been addressed

generalized tanh method with symbolic computation and generalized shallow water wave equation abstract we report that symbolic computation with the generalized tanh method leads to new soliton like solutions for a 2 1 dimensional generalization of the shallow water wave equations

on the existence of optimal controls the optimal control problem where the state is governed by an ito stochastic differential equation possibly just an ordinary differential equation is formulated in martingale terms under a coercivity condition which is weaker than compactness of the control set a convexity condition and mild continuity hypotheses on the data it is shown by the direct method that optimal controls exist hard and soft constraints are allowed in the absence of soft constraints it is shown that there exists an optimal control that is a function only of the present time and state i e the synthesis problem has a solution the main tool here is krylov s markovian selection theorem

singular optimal stochastic controls i existence we apply the compactification method to study the control problem where the state is governed by an ito stochastic differential equation allowing both classical and singular control the problem is reformulated as a martingale problem on an appropriate canonical space after the relaxed form of the classical control is introduced under some mild continuity hypotheses on the data it is shown by purely probabilistic arguments that an optimal control for the problem exists the value function is shown to be borel measurable

construction and decomposition of reflecting diffusions on lipschitz domains with holder cusps we consider a d dimensional euclidean domain d whose boundary is lipschitz continuous but admits locally finite number of outward or inward holder cusp points using a method of stampacchia and moser for pde we first construct a conservative diffusion process on the euclidean closure of d possessing a strong feller resolvent and associated with a second order uniformly elliptic differential operator of divergence form with measurable coefficients a ij the sample path of the constructed diffusion can be uniquely decomposed as a sum of a martingale additive functional and an additive functional locally of zero energy the second additive functional will be proved to be of bounded variation with a skorohod type expression whenever a ij is weakly differentiable and the holder exponent at each outward cusp boundary point is greater than 1 2 regardless the dimension d

symbolic computation and new families of exact soliton like solutions to the integrable broer kaup bk equations in 2 1 dimensional spaces in this paper new families of soliton like solutions are obtained for 2 1 dimensional integrable broer kaup equations by using the symbolic computation method developed by gao and tian sample solutions obtained from these methods are presented solitary wave solutions are merely a special case in one family the method can also be extended to other types of nonlinear evolution equations in mathematical physics

dynamical survey of the dual power zakharov kuznetsov burgers equation with external periodic perturbation abstract we investigate the dynamical behavior of the newly introduced dual power zakharov kuznetsov burgers equation using bifurcation theory of planar dynamical systems we study bifurcations of traveling wave solutions of the dual power zakharov kuznetsov burgers equation in presence and absence of viscosity effect in presence of an external periodic perturbation we discuss the periodic and chaotic motions of the perturbed dual power zakharov kuznetsov burgers equation by analyzing phase projection analysis time series analysis poincare section and sensitivity analysis the effect of viscosity plays an important role in the transition from chaotic motion to periodic motion of the perturbed dual power zakharov kuznetsov burgers equation

singular optimal controls of stochastic recursive systems and hamilton jacobi bellman inequality abstract in this paper we study the optimal singular controls for stochastic recursive systems in which the control has two components the regular control and the singular control under certain assumptions we establish the dynamic programming principle for this kind of optimal singular controls problem and prove that the value function is a unique viscosity solution of the corresponding hamilton jacobi bellman inequality in a given class of bounded and continuous functions at last an example is given for illustration

symbolic computation backlund transformation and analytic n soliton like solution for a nonlinear schrodinger equation with nonuniformity term from certain space laboratory plasmas abstract with symbolic computation a bilinear backlund transformation is presented for a nonlinear schrodinger equation with nonuniformity term from certain space laboratory plasmas and correspondingly the one soliton like solution is derived from the backlund transformation simultaneously the n soliton like solution in double wronskian form is also given besides the authors verify that the n 1 and n soliton like solutions satisfy the backlund transformation the results obtained in this paper might be valuable for the study of the nonuniform media

a generalized f expansion method with symbolic computation exactly solving broer kaup equations abstract in this paper a generalized f expansion method is applied to construct exact solutions of the 2 1 dimensional broer kaup equations as a result many general exact non travelling wave and coefficient function solutions are obtained including single and combined non degenerate jacobi elliptic function solutions soliton like solutions and trigonometric function solutions each of which contains two arbitrary functions compared with most existing f expansion methods the proposed method gives new and more general exact solutions more importantly with the aid of symbolic computation the method provides a powerful mathematical tool to solve a large many nonlinear partial differential equations

generalized kuhn tucker conditions for n firm stochastic irreversible investment under limited resources in this paper we study a continuous time optimal stochastic investment problem under limited resources in a market with n firms the investment processes are subject to a time dependent stochastic constraint rather than using a dynamic programming approach we exploit the concavity of the profit functional to derive some necessary and sufficient first order conditions for the corresponding social planner optimal policy our conditions are a stochastic infinite dimensional generalization of the kuhn tucker theorem the lagrange multiplier takes the form of a nonnegative optional random measure on 0 t which is flat off the set of times for which the constraint is binding i e when all the fuel is spent as a subproduct we obtain an enlightening interpretation of the first order conditions for a single firm in bank siam j control optim 44 2005 pp 1529 1541 in the infinite horizon case with operating profit functions of cobb douglas type our method allows the explicit calculation of t

reflecting brownian motion in a cusp let c be the cusp x y x 0 x y x where 1 set c 1 x y x 0 y x and c 2 x y x 0 y x we study the existence and uniqueness in law of reflecting brownian motion in c the angle of reflection at c j 0 relative to the inward unit normal is a constant j 2 2 and is positive iff the direction of reflection has a negative first component in all sufficiently small neighborhoods of 0 when 1 2 0 existence and uniqueness in law hold when 1 2 0 existence fails we also obtain results for a large class of asymmetric cusps we make essential use of results of warschawski on the differentiability at the boundary of conformal maps

application of exp function method to the whitham broer kaup shallow water model using symbolic computation in this letter the exp function method is applied to the whitham broer kaup shallow water model with the help of symbolic computation several kinds of new solitary wave solutions are formally derived

multi solitonic solutions for the variable coefficient variant boussinesq model of the nonlinear water waves abstract for the nonlinear and dispersive long gravity waves traveling in two horizontal directions with varying depth of the water we consider a variable coefficient variant boussinesq vcvb model with symbolic computation we construct the connection between the vcvb model and a variable coefficient ablowitz kaup newell segur vcakns system under certain constraints using the n fold darboux transformation of the vcakns system we present two sets of multi solitonic solutions for the vcvb model which are expressed in terms of the vandermonde like and double wronskian determinants respectively dynamics of those solutions are analyzed and graphically discussed such as the parallel solitonic waves shape changing collision head on collision fusion fission behavior and elastic fusion coupled interaction

soliton like solutions of a generalized variable coefficient higher order nonlinear schrodinger equation from inhomogeneous optical fibers with symbolic computation for the long distance communication and manufacturing problems in optical fibers the propagation of subpicosecond or femtosecond optical pulses can be governed by the variable coefficient nonlinear schrodinger equation with higher order effects such as the third order dispersion self steepening and self frequency shift in this paper we firstly determine the general conditions for this equation to be integrable by employing the painleve analysis based on the obtained 3 3 lax pair we construct the darboux transformation for such a model under the corresponding constraints and then derive the nth iterated potential transformation formula by the iterative process of darboux transformation through the one and two soliton like solutions we graphically discuss the features of femtosecond solitons in inhomogeneous optical fibers

analytic n solitary wave solution of a variable coefficient gardner equation from fluid dynamics and plasma physics in this paper the investigation is focused on a variable coefficient gardner equation with quadric and cubic nonlinearities from fluid dynamics and plasma physics using the hirota bilinear method the one two and three solitary wave solutions of the variable coefficient gardner equation are derived and the analytic n solitary wave solution is presented for the first time in this paper with the aid of symbolic computation figures are plotted to illustrate the solutions obtained in this paper

solitonic solutions for a variable coefficient variant boussinesq system in the long gravity waves variable coefficient variant boussinesq vcvb system is able to describe the nonlinear and dispersive long gravity waves traveling in two horizontal directions with varying depth in this paper with symbolic computation a lax pair associated with the vcvb system under some constraints for variable coefficients is derived and based on the lax pair two sorts of basic darboux transformations are presented by applying the darboux transformations some solitonic solutions are obtained with the relevant constraints given in the text in addition the vcvb system is transformed to a variable coefficient broer kaup system solitonic solutions and procedure of getting them could be helpful to solve the nonlinear and dispersive problems in fluid dynamics

exact solutions of the two dimensional burgers equation soliton like solutions of the two dimensional burgers equation are obtained some new solutions from soliton like solutions are also presented

optimal consumption for general diffusions with absorbing and reflecting barriers two stochastic control problems of the storage or inventory type are considered for general diffusion processes in the absorption problem a diffusion process is controlled by subtracting a nondecreasing withdrawal process the controlled process is absorbed if it reaches zero the objective function to be maximized is the expected discounted value of the withdrawals plus a discounted penalty for absorption in the reflection problem the process can be controlled by subtracting a withdrawal process and adding a deposit process and the controlled process must be nonnegative one seeks to maximize an expected discounted weighted difference in withdrawals and deposits the value function is computed and a necessary and sufficient condition for the existence of an optimal policy is given when they exist optimal policies are found to be the minimal processes which keep the controlled process inside an interval

infinitely many symmetries of the davey stewartson equation using a formal series symmetry method for the davey stewartson equation dse we find that there exist two sets of infinitely many formal series symmetries of the dse however different from the kadomtsev petviashvili equation kpe we failed to get infinitely many truncated symmetries only six truncated symmetries can be obtained simply from the formal series symmetries

singular stochastic control problems in this paper we study an optimal singular stochastic control problem by using a time transformation this problem is shown to be equivalent to an auxiliary control problem defined as a combination of an optimal stopping problem and a classical control problem for this auxiliary control problem the controller must choose a stopping time optimal stopping and the new control variables belong to a compact set this equivalence is obtained by showing that the discontinuous state process governed by a singular control is given by a time transformation of an auxiliary state process governed by a classical bounded control it is proved that the value functions for these two problems are equal for a general form of the cost the existence of an optimal singular control is established under certain technical hypotheses moreover the problem of approximating singular optimal control by absolutely continuous controls is discussed in the same class of admissible controls

a transformation with symbolic computation and abundant new soliton like solutions for the 1 2 dimensional generalized burgers equation in this paper an auto backlund transformation is presented for the generalized burgers equation ut uxy uuy ux 1xuy 0 is constant by using an ansatz and symbolic computation particularly this equation is transformed into a 1 2 dimensional generalized heat equation t xy 0 by the cole hopf transformation this shows that this equation is c integrable abundant types of new soliton like solutions are obtained by virtue of the obtained transformation these solutions contain n soliton like solutions shock wave solutions and singular soliton like solutions which may be of important significance in explaining some physical phenomena the approach can also be extended to other types of nonlinear partial differential equations in mathematical physics

singular control of stochastic linear systems with recursive utility we formulate a class of singular stochastic control problem with recursive utility where the cost function is determined by a backward stochastic differential equation some characteristics of the value function of the control problem are obtained by the method of approximation via penalization and the optimal control process is constructed

the numerical simulation for stiff systems of ordinary differential equations in this paper the variational iteration method is applied to solve systems of ordinary differential equations in both linear and nonlinear cases focusing interest on stiff problems some examples are given to illustrate the accuracy and effectiveness of the method we compare our results with results obtained by the adomian decomposition method this comparison reveals that the variational iteration method is easier to be implemented in fact the variational iteration method is a promising method to various systems of linear and nonlinear equations

lax pair backlund transformation and n soliton like solution for a variable coefficient gardner equation from nonlinear lattice plasma physics and ocean dynamics with symbolic computation abstract in this paper a generalized variable coefficient gardner equation arising in nonlinear lattice plasma physics and ocean dynamics is investigated with symbolic computation the lax pair and backlund transformation are explicitly obtained when the coefficient functions obey the painleve integrable conditions meanwhile under the constraint conditions two transformations from such an equation either to the constant coefficient gardner or modified korteweg de vries mkdv equation are proposed via the two transformations the investigations on the variable coefficient gardner equation can be based on the constant coefficient ones the n soliton like solution is presented and discussed through the figures for some sample solutions it is shown in the discussions that the variable coefficient gardner equation possesses the right and left travelling soliton like waves which involve abundant temporally inhomogeneous features

backlund transformation lax pair and solutions for the caudrey dodd gibbon equation by using bell polynomials and symbolic computation we investigate the caudrey dodd gibbon equation analytically through a generalization of bells polynomials its bilinear form is derived based on which the periodic wave solution and soliton solutions are presented and the soliton solutions with graphic analysis are also given furthermore backlund transformation and lax pair are derived via the bells exponential polynomials finally the ablowitz kaup newell segur system is constructed

painleve analysis and new analytic solutions for variable coefficient kadomtsev petviashvili equation with symbolic computation abstract the variable coefficient kadomtsev petviashvili kp equation is hereby under investigation painleve analysis is given out and an auto backlund transformation is presented via the truncated painleve expansion based on the auto backlund transformation new analytic solutions are given including the soliton like and periodic solutions it is also reduced to a 1 1 dimensional partial differential equation via classical lie group method and the painleve i equation by ck direct method

brownian motion in a wedge with variable skew reflection does planar brownian motion confined to a wedge by skew reflection on the sides approach the vertex of the wedge this question has been answered by varadhan and williams in the case where the direction of reflection is constant on each of the sides but here we address the question when the direction reflected is allowed to vary a necessary condition and a sufficient condition are obtained for the vertex to be reached the conditions are of a geometric nature and the gap between them is quite small

optimal control of inflation a central bank problem this paper models the action of the central bank on the dynamics of the nominal interest rate with the aim of controlling inflation the problem is set up as a two dimensional bounded variation control problem it is shown that its variational formulation leads to a stochastic differential game with stopping times between the conservative and the expansionist tendencies of the bank

on the semimartingale representation of reflecting brownian motion in a cusp letc be the symmetric cusp x y 2 x y x x 0 where 1 in this paper we decide whether or not reflecting brownian motion inc has a semimartingale representation here the reflecting brownian motion has directions of reflection that make constant angles with the unit inward normals to the boundary our results carry through for a wide class of asymmetric cusps too

painleve analysis auto backlund transformations and exact solutions for a simplified model for reacting mixtures abstract recently a simplified model for reacting mixtures was investigated to admit the potential symmetries only when the structure function f u in the model was of the form u 2 k in this paper we investigate some other properties of the nonlinear model with the condition f u u 2 k firstly the painleve analysis is performed such that it is shown that this equation passes the painleve test and then two new types of auto backlund transformations abts are found by using the truncated painleve expansion analysis and some ansatz the abts reduce the nonlinear model to the systems of linear partial differential equations with respect to the new introduced variables finally based on the obtained auto backlund transformations we explore some explicit exact solutions including soliton solutions singular soliton solutions soliton like solutions rational solutions and other types of solutions which may be useful to explain the corresponding physical phenomena

new applications of variational iteration method abstract the variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled schrodinger kdv generalized kdv and shallow water equations the exact and numerical solutions obtained by variational iteration method are compared with that obtained using adomian decomposition method the comparison shows that the two solutions obtained are excellent agreement the method is made showing that the former is more effective than the latter in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

dynamical survey of a generalized zakharov equation and its exact travelling wave solutions we investigate the dynamical behavior of a generalized zakharov equation for the complex envelope of the high frequency wave and the real low frequency field by analyzing its phase portraits following a dynamical system approach in different parameter regions we depict phase portraits of a travelling wave system through discussing the bifurcation of phase portraits we unwrap explicit miscellaneous travelling waves including localized and periodic ones

new family of overturning soliton solutions for a typical breaking soliton equation the breaking soliton equations are of current interest while the application of computer algebra to sciences has a bright future in this paper a new family of overturning soliton solutions for a typical breaking soliton equation is obtained via a computer algebra based method an example of explicit solutions from the family is given solitary waves are also shown to be merely a simple case belonging to the family

new solitonic solutions to a 3 1 dimensional jimbo miwa equation abstract performing computerized symbolic computation we are able to present new analytic solutions of a 3 1 dimensional jimbo miwa equation which does not pass any of the conventional integrability tests applying the generalized tanh method we have found such exact solutions as both the nontraveling solitonic and traveling solitary waves

jacobi elliptic function solutions of nonlinear wave equations via the new sinh gordon equation expansion method in this paper based on the well known sinh gordon equation a new sinh gordon equation expansion method is developed this method transforms the problem of solving nonlinear partial differential equations into the problem of solving the corresponding systems of algebraic equations with the aid of symbolic computation the procedure can be carried out by computer many nonlinear wave equations in mathematical physics are chosen to illustrate the method such as the kdv mkdv equation 2 1 dimensional coupled davey stewartson equation the new integrable davey stewartson type equation the modified boussinesq equation 2 1 dimensional mkp equation and 2 1 dimensional generalized kdv equation as a consequence many new doubly periodic jacobian elliptic function solutions are obtained when the modulus m 1 or 0 the corresponding solitary wave solutions and singly periodic solutions are also found this approach can also be applied to solve other nonlinear differential equations

connections between optimal stopping and singular stochastic control i monotone follower problems the stochastic control problem of tracking a brownian motion by a nondecreasing process monotone follower is related to a question of optimal stopping direct probabilistic arguments are employed to show that the two problems are equivalent and that both admit optimal solutions

maximum principle for singular stochastic control problems in this paper an optimal singular stochastic control problem is considered for this model a general stochastic maximum principle is obtained by using a time transformation this is the first version of the stochastic maximum principle that covers nonlinear cases

soliton solutions and a backlund transformation for a generalized nonlinear schrodinger equation with variable coefficients from optical fiber communications under investigation in this paper is a generalized nonlinear schrodinger model with variable dispersion nonlinearity and gain loss which could describe the propagation of optical pulse in inhomogeneous fiber systems by employing the hirota method one and two soliton solutions are obtained with the aid of symbolic computation furthermore a general formula which denotes multi soliton solutions is given some main properties of the solutions are discussed simultaneously as one important property of nonlinear evolution equation the backlund transformation in bilinear form is also constructed which is helpful on future research and as far as we know is firstly proposed in this paper