benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

a limited memory bfgs type method for large scale unconstrained optimization in this paper a new numerical method for solving large scale unconstrained optimization problems is presented it is derived from a modified bfgs type update formula by wei li and qi it is observed that the update formula can be extended to the framework of limited memory scheme with hardly more storage or arithmetic operations under some suitable conditions the global convergence property is established the implementations of the method on a set of cute problems indicate that this extension is beneficial to the performance of the algorithm

global convergence of a cass of quasi newton methods on convex problems we study the global convergence properties of the restricted broyden class of quasi newton methods when applied to a convex objective function we assume that the line search satisfies a standard sufficient decrease condition and that the initial hessian approximation is any positive definite matrix we show global and superlinear convergence for this class of methods except for dfp this generalizes powell s well known result for the bfgs method the analysis gives us insight into the properties of these algorithms in particular it shows that dfp lacks a very desirable self correcting property possessed by bfgs

a tool for the analysis of quasi newton methods with application to unconstrained minimization the bfgs update formula is shown to have an important property that is inde pendent of the algorithmic context of the update and that is relevant to both constrained and unconstrained optimization the bfgs method for unconstrained optimization using a variety of line searches including backtracking is shown to be globally and superlinearly convergent on uniformly convex problems the analysis is particularly simple due to the use of some new tools introduced in this paper

on convergence of solutions to equilibria for quasilinear parabolic problems abstract we show convergence of solutions to equilibria for quasilinear parabolic evolution equations in situations where the set of equilibria is non discrete but forms a finite dimensional c 1 manifold which is normally hyperbolic our results do not depend on the presence of an appropriate lyapunov functional as in the ojasiewicz simon approach but are of local nature

a modified quasi newton method for nonlinear equations abstract in this paper a modified quasi newton method is proposed for solving the nonlinear equation f x 0 which is based on a new quasi newton approach the usual quasi newton equation is b k 1 s k y k where s k x k 1 x k y k f x k 1 f x k the new quasi newton equation is b k 1 s k y k in which s k is based on the iterates x k 1 x k x k 1 and y k is based on the function values f x k 1 f x k f x k 1 the new quasi newton equation exploits additional information by assuming a quadratic relationship between the information from the last three iterates the modified quasi newton method is based on the new quasi newton equation and possess local superlinear convergence properties numerical experiments show that the modified quasi newton method is promising

on the maximal lp lq regularity of solutions to a general linear parabolic system abstract we show the existence of solution in the maximal l p l q regularity framework to a class of symmetric parabolic problems on a uniformly c 2 domain in r n our approach consist in showing r boundedness of families of solution operators to corresponding resolvent problems first in the whole space then in half space perturbed half space and finally using localization arguments on the domain assuming additionally boundedness of the domain we also show exponential decay of the solution in particular our approach does not require assuming a priori the uniform lopatinskii shapiro condition

solitonic excitations and interactions in an α helical protein modeled by three coupled nonlinear schrodinger equations with variable coefficients governing the molecular excitations associated with bioenergy transport in an helical protein through the soliton modes three coupled higher order nonlinear schrodinger equations with variable coefficients are investigated via symbolic computation using bell polynomials a bilinear form and backlund transformation are derived for this model furthermore explicit n soliton solutions are constructed in terms of the double wronskian determinant solitonic excitations are found to remain stable against the disorders of the parameters under certain constraints finally propagation characteristics and interactions of the solitonic excitations are discussed soliton amplitudes are related to the energy modulation coefficients and both the soliton properties and energy distribution during the interactions are affected by the inhomogeneity coefficients of the protein with time dependent disorders

backlund transformation and solutions of a 3 1 dimensional nonlinear evolution equation in this paper bell polynomial method is used to study the integrability of a 3 1 dimensional nonlinear evolution equation we get the bilinear representation and backlund transformation of the equation the exact solutions are obtained by means of linear superposition principle and homoclinic test approach

abundant lump type solutions of the jimbo miwa equation in 3 1 dimensions abstract based on the hirota bilinear form of the 3 1 dimensional jimbo miwa equation ten classes of its lump type solutions are generated via maple symbolic computations whose analyticity can be easily achieved by taking special choices of the involved parameters those solutions supplement the existing lump type solutions presented previously in the literature

wronskian and grammian solutions for a 2 1 dimensional date jimbo kashiwara miwa equation abstract in this paper a 2 1 dimensional date jimbo kashiwara miwa equation is investigated based on the hirota method and auxiliary variable backlund transformation is obtained under certain conditions the hirota bilinear forms can be reduced to the plucker and jacobi identities via the wronskian and grammian solutions through the wronskian technique and pfaffian derivative formulae n soliton solutions in the wronskian and grammian are given graphically presented soliton collisions are elastic both in the wronskian and grammian and after each collision the solitons keep their amplitudes unchanged except for the phase shifts

bell polynomial manipulations on the backlund transformations and lax pairs for some soliton equations with one tau function in the framework of bell polynomial manipulations under investigation hereby are three single field bilinearizable equations the 1 1 dimensional shallow water wave model boiti leon manna pempinelli model and 2 1 dimensional sawada kotera model based on the concept of scale invariance a direct and unifying bell polynomial scheme is employed to achieve the backlund transformations and lax pairs associated with those three soliton equations note that the bell polynomial expressions and bell polynomial typed backlund transformations for those three soliton equations can be respectively cast into the bilinear equations and bilinear backlund transformations with symbolic computation consequently it is also shown that the bell polynomial typed backlund transformations can be linearized into the corresponding lax pairs

bell polynomial approach applied to the seventh order sawada kotera ito equation in this paper the bell polynomial approach is extended to the seventh order sawada kotera ito equation which is regarded as a higher order integrable one in the korteweg de vries hierarchy through several combinations of the constructed bell polynomials the bilinear form with an auxiliary independent variable introduced backlund transformation lax pair and infinite conservation laws for such an equation are derived by means of symbolic computation

a globally and superlinearly convergent gauss newton based bfgs method for symmetric nonlinear equations in this paper we present a gauss newton based bfgs method for solving symmetric nonlinear equations which contain as a special case an unconstrained optimization problem a saddle point problem and an equality constrained optimization problem a suitable line search is proposed with which the presented bfgs method exhibits an approximate norm descent property under appropriate conditions global convergence and superlinear convergence of the method are established the numerical results show that the proposed method is successful

diversity of interaction solutions to the 2 1 dimensional ito equation abstract we aim to show the diversity of interaction solutions to the 2 1 dimensional ito equation based on its hirota bilinear form the proof is given through maple symbolic computations an interesting characteristic in the resulting interaction solutions is the involvement of an arbitrary function special cases lead to lump solutions lump soliton solutions and lump kink solutions two illustrative examples of the resulting solutions are displayed by three dimensional plots and contour plots

new quasi newton methods for unconstrained optimization problems abstract many methods for solving minimization problems are variants of newton method which requires the specification of the hessian matrix of second derivatives quasi newton methods are intended for the situation where the hessian is expensive or difficult to calculate quasi newton methods use only first derivatives to build an approximate hessian over a number of iterations this approximation is updated each iteration by a matrix of low rank in unconstrained minimization the original quasi newton equation is bk 1sk yk where yk is the difference of the gradients at the last two iterates in this paper we first propose a new quasi newton equation b k 1 s k y k in which y k is decided by the sum of yk and aksk where ak is some matrix then we give two choices of ak which carry some second order information from the hessian of the objective function the three corresponding bfgs type algorithms are proved to possess global convergence property the superlinear convergence of the one algorithm is proved extensive numerical experiments have been conducted which show that the proposed algorithms are very encouraging

improved bell polynomial procedure for the higher order korteweg de vries equations in fluid dynamics korteweg de vries kdv typed equations are seen in fluid dynamics plasma physics and other fields by means of the bell polynomial procedure we take two higher order members of the kdv hierarchy the seventh and ninth order lax s kdv equations in fluid dynamics as the examples for studying the integrable properties of the higher order equations different from lower order equations two new partial differential operators in the bell polynomial procedure are introduced to construct the multi dimensional bilinear forms of such equations with several auxiliary independent variables through the procedure simplified via the algebraic operation of the polynomials the backlund transformations lax pairs and infinite conservation laws of such equations are deduced

on bilinear representations and infinite conservation laws of a nonlinear variable coefficient equation the kdv equation for non uniform media with relaxation effects has extensive applications in mathematics and physics satsuma 1976 20 and hirota 1979 21 once investigated its algebraic properties in the paper we shall generalize it a more general integrable equation with variable coefficients and further discuss the corresponding bilinear representation backlund transformation lax pair and infinite conservation laws by making use of the bell polynomials

two modified scaled nonlinear conjugate gradient methods following the scaled conjugate gradient methods proposed by andrei we hybridize the memoryless bfgs preconditioned conjugate gradient method suggested by shanno and the spectral conjugate gradient method suggested by birgin and martinez based on a modified secant equation suggested by yuan and propose two modified scaled conjugate gradient methods the interesting features of our methods are applying the function values in addition to the gradient values and satisfying the sufficient descent condition for the generated search directions which leads to the global convergence for uniformly convex functions numerical comparisons between the implementations of one of our methods which generates descent search directions for general functions and an efficient scaled conjugate gradient method proposed by andrei are made on a set of unconstrained optimization test problems from the cuter collection using the performance profile introduced by dolan and more

rational solutions to a kdv like equation two classes of rational solutions to a kdv like nonlinear differential equation are constructed the basic object is a generalized bilinear differential equation based on a prime number p 3 a conjecture is made that the two presented classes of rational solutions contain all rations solutions to the considered kdv like equation which are generated from polynomial solutions to the corresponding generalized bilinear equation

an adaptive three term conjugate gradient method based on self scaling memoryless bfgs matrix abstract due to its simplicity and low memory requirement conjugate gradient methods are widely used for solving large scale unconstrained optimization problems in this paper we propose a three term conjugate gradient method the search direction is given by a symmetrical perry matrix which contains a positive parameter the value of this parameter is determined by minimizing the distance of this matrix and the self scaling memoryless bfgs matrix in the frobenius norm the sufficient descent property of the generated directions holds independent of line searches the global convergence of the given method is established under wolfe line search for general non convex functions numerical experiments show that the proposed method is promising

properties and numerical performance of quasi newton methods with modified quasi newton equations quasi newton qn equation plays a core role in contemporary nonlinear optimization the usual qn equation employs only the gradients but ignores the available function value information in this paper we derive a class of modified qn equations with a vector parameter which use both available gradient and function value information the modified quasi newton methods maintain most properties of the usual quasi newton methods meanwhile they achieve a higher order accuracy in approximating the second order curvature of the problem functions than the usual ones do numerical experiments are reported which support the theoretical analyses and show the advantages of the modified qn methods over the usual ones

bell polynomial approach and n soliton solution for the extended lotka volterra equation in plasmas symbolically investigated in this paper is the extended lotka volterra elv equation which can govern the kinetics of the discrete peaks of the weak langmuir turbulence in plasmas without the linear damping and random noise binary bell polynomials are applied to the bilinearization of the discrete system bilinear backlund transformation of the elv equation is constructed n soliton solution in terms of the extended casorati determinant is also presented and verified propagation and interaction behaviors of the langmuir turbulence are analyzed it is demonstrated that the number of the interacting langmuir waves can influence the soliton velocity and amplitude as well as the collision phase shift graphic illustrations of the solitonic collisions show that the repulsion effects and nonlinear interactions are also associated with the number of the interacting langmuir waves

analytic solutions for the 2 1 dimensional generalized sine gordon equations in nonlinear optics abstract the 2 1 dimensional generalized sine gordon equations can be used to describe the propagation of femtosecond laser pulse in a systems of two level atoms in this paper bilinear forms of the equations have been constructed through variable transformation and bell polynomial based on the bilinear method and truncated painleve expansion multi soliton and quasi periodic peakon solutions for such a system are derived respectively overtaking elastic interactions between the two solitons and among the three solitons have been found it is presented that the soliton with the smaller amplitude can travel faster than the larger one apart from the soliton other type of nonlinear wave propagating in the systems of two level atoms has been displayed namely the quasi periodic peakon the peakon oscillates in both space and time while its left and right derivatives at peak point are relatively large which means the electric field intensity of the femtosecond laser pulse is rather strong

negative order korteweg de vries equations in this paper based on the regular korteweg de vries kdv system we study negative order kdv nkdv equations particularly their hamiltonian structures lax pairs conservation laws and explicit multisoliton and multikink wave solutions thorough bilinear backlund transformations the nkdv equations studied in our paper are differential and actually derived from the first member in the negative order kdv hierarchy the nkdv equations are not only gauge equivalent to the camassa holm equation through reciprocal transformations but also closely related to the ermakov pinney systems and the kupershmidt deformation the bi hamiltonian structures and a darboux transformation of the nkdv equations are constructed with the aid of trace identity and their lax pairs respectively the single and double kink wave and bell soliton solutions are given in an explicit formula through the darboux transformation the one kink wave solution is expressed in the form of tanh while the one bell soliton is in the form of sech and both forms are very standard the collisions of two kink wave and two bell soliton solutions are analyzed in detail and this singular interaction differs from the regular kdv equation multidimensional binary bell polynomials are employed to find bilinear formulation and backlund transformations which produce n soliton solutions a direct and unifying scheme is proposed for explicitly building up quasiperiodic wave solutions of the nkdv equations furthermore the relations between quasiperiodic wave solutions and soliton solutions are clearly described finally we show the quasiperiodic wave solution convergent to the soliton solution under some limit conditions

several efficient gradient methods with approximate optimal stepsizes for large scale unconstrained optimization abstract in this paper we introduce a new concept of approximate optimal stepsize for gradient method use it to interpret the nice numerical effect of the barzilai borwein bb method and present several efficient gradient methods with approximate optimal stepsizes for large scale unconstrained optimization based on revising some modified bfgs update formulae we construct some new quadratic approximation models to develop several approximate optimal stepsizes it is remarkable that these approximate optimal stepsizes lie in the intervals which contain the two well known bb stepsizes we then truncate these approximate optimal stepsizes by the two well known bb stepsizes and treat the resulted approximate optimal stepsizes as the new stepsizes for gradient methods moreover for the nonconvex case we also design a new approximation model to generate an approximate optimal stepsize for gradient methods we establish the convergences of the proposed methods under weaker condition numerical results show that the proposed methods are very promising

notes on the dai yuan yuan modified spectral gradient method in this paper we give some notes on the two modified spectral gradient methods which were developed in 10 these notes present the relationship between their stepsize formulae and some new secant equations in the quasi newton method in particular we also introduce another two new choices of stepsize by using an efficient nonmonotone line search technique we propose some new spectral gradient methods under some mild conditions we show that these proposed methods are globally convergent numerical experiments on a large number of test problems from the cuter library are also reported which show that the efficiency of these proposed methods

binary bell polynomials hirota bilinear approach to levi equation combining the binary bell polynomials and hirota method we obtained two kinds of equivalent bilinear equations for the levi equation then we got the double wronskian solutions of the levi equation by virtue of one of the bilinear equations furthermore we constructed the bilinear backlund transformation and the lax pair finally we also derived the darboux transformation and the infinite conservation laws of the levi equation

improved hessian approximation with modified secant equations for symmetric rank one method symmetric rank one sr1 is one of the competitive formulas among the quasi newton qn methods in this paper we propose some modified sr1 updates based on the modified secant equations which use both gradient and function information furthermore to avoid the loss of positive definiteness and zero denominators of the new sr1 updates we apply a restart procedure to this update three new algorithms are given to improve the hessian approximation with modified secant equations for the sr1 method numerical results show that the proposed algorithms are very encouraging and the advantage of the proposed algorithms over the standard sr1 and bfgs updates is clearly observed

rational solutions to two new kp like equations in this paper we will present a new 3 1 dimensional kp like nonlinear partial differential equation and construct the rational solutions to this new 3 1 dimensional kp like equation the proposed method in this work is based on a generalized bilinear differential equation which implies that we can build the rational solutions to the presented kp like equation from polynomial solutions to the aforementioned generalized bilinear equation moreover for y z this new model reduces to the new 2 1 dimensional kp like nonlinear partial differential equation which will be studied as well herein

integrability of the modified generalised vakhnenko equation integrability of the modified generalised vakhnenko equation is investigated systematically based on binary bell polynomials its bilinear representation n soliton solutions bilinear backlund transformation and lax pair are succinctly constructed moreover the conservation laws of the modified generalised vakhnenko equation are discussed by using corresponding lax pair furthermore the quasiperiodic solution of the modified generalised vakhnenko equation is presented by applying hirota direct method and riemann theta function the asymptotic behavior of the one periodic wave is analyzed in details it is shown that the one periodic wave solution tends to the one soliton solution under a small amplitude limit 0 finally the new n soliton solutions of the standard vakhnenko equation are presented it would be specially mentioned that all the results of modified generalised vakhnenko equation can be reduced to the generalised vakhnenko equation and standard vakhnenko equation under the special case of 1 and 1 0 respectively

on the combinatorics of the hirota d operators a generic formula is presented which relates the hirota d operators to simple combinatorics particular classes of partition polynomials bell polynomials and generalizations are found to play an important role in the characterization of bilinearizable equations as a consequence it is shown that bilinear backlund transformations for single field bilinearizable equations linearize systematically into corresponding laxpairs

bilinear backlund transformations kink periodic solitary wave and lump wave solutions of the bogoyavlenskii kadomtsev petviashvili equation abstract this paper investigates the bogoyavlenskii kadomtsev petviashvili equation by using the binary bell polynomials method and differential constraint technique several kinds of more general bilinear representations and baklund transformations are presented at the same time multiple wave solutions including the kink periodic solitary wave and bright dark lump wave solutions are constructed the resonant interactions between two kink solitary waves are investigated and exhibited mathematically and graphically lump wave solutions a kind of rational function localized in all directions of the space are obtained by the taylor expansion of the kink periodic solitary wave also we discuss the dynamical behavior of the lump wave solutions and their structures

reaction diffusion systems of maxwell stefan type with reversible mass action kinetics abstract the mass based maxwell stefan approach to one phase multicomponent reactive mixtures is mathematically analyzed it is shown that the resulting quasilinear strongly coupled reaction diffusion system is locally well posed in an l p setting and generates a local semiflow on its natural state space solutions regularize instantly and become strictly positive if their initial components are all nonnegative and nontrivial for a class of reversible mass action kinetics the positive equilibria are identified these are precisely the constant chemical equilibria of the system which may form a manifold here the total free energy of the system is employed which serves as a lyapunov function for the system by the generalized principle of linearized stability positive equilibria are proved to be normally stable

on hager and zhang s conjugate gradient method with guaranteed descent abstract in this paper we point out that hager zhang family of conjugate gradient methods are based on the spectral scaling secant equation are really members of dai liao type of gradient methods with common constant parameters we propose a possible efficient parameter for hager zhang s conjugate gradient method with guaranteed descent cg descent and present a conjugate gradient method cg descent1 the cg descent1 method preserves the same global convergence properties as cg descent method of hager and zhang and is numerically tested compared with cg descent method and other conjugate gradient methods considering the difference of the search directions approximation to the search direction of the memoryless bfgs method we give the reason why the proposed method is more efficient than cg descent method under some conditions and further find an optimal conjugate gradient method and an approximation optimal conjugate method in hager zhang family of conjugate gradient methods

a modified polak ribiere polyak conjugate gradient algorithm for nonsmooth convex programs the conjugate gradient cg method is one of the most popular methods for solving smooth unconstrained optimization problems due to its simplicity and low memory requirement however the usage of cg methods is mainly restricted to solving smooth optimization problems so far the purpose of this paper is to present efficient conjugate gradient type methods to solve nonsmooth optimization problems by using the moreau yosida regulation smoothing approach and a nonmonotone line search technique we propose a modified polak ribiere polyak prp cg algorithm for solving a nonsmooth unconstrained convex minimization problem our algorithm possesses the following three desired properties i the search direction satisfies the sufficient descent property and belongs to a trust region automatically ii the search direction makes use of not only the gradient information but also the function value information and iii the algorithm inherits an important property of the well known prp method the tendency to turn towards the steepest descent direction if a small step is generated away from the solution preventing a sequence of tiny steps from happening under standard conditions we show that the algorithm converges globally to an optimal solution numerical experiment shows that our algorithm is effective and suitable for solving large scale nonsmooth unconstrained convex optimization problems

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

darboux covariant lax pairs and infinite conservation laws of the 2 1 dimensional breaking soliton equation in this paper the binary bell polynomials are applied to succinctly construct bilinear formulism bilinear backlund transformations lax pairs and darboux covariant lax pairs for the 2 1 dimensional breaking soliton equation an extra auxiliary variable is introduced to get the bilinear formulism the infinitely local conservation laws of the equation are found by virtue of its lax equation and a generalized miura transformation all conserved densities and fluxes are given with explicit recursion formulas

new quasi newton methods via higher order tensor models many researches attempt to improve the efficiency of the usual quasi newton qn methods by accelerating the performance of the algorithm without causing more storage demand they aim to employ more available information from the function values and gradient to approximate the curvature of the objective function in this paper we derive a new qn method of this type using a fourth order tensor model and show that it is superior with respect to the prior modification of wei et al 2006 4 convergence analysis gives the local convergence property of this method and numerical results show the advantage of the modified qn method

binary bell polynomial manipulations on the integrability of a generalized 2 1 dimensional korteweg de vries equation abstract this paper investigates the integrability of a generalized 2 1 dimensional korteweg de vries equation with the aid of binary bell polynomials its bilinear formalism bilinear backlund transformation lax pair and darboux covariant lax pair are succinctly constructed which can be reduced to the ones of several integrable equations such as the korteweg de vries equation and the calogero bogoyavlenskii schiff equation moreover the infinite conservation laws of the generalized 2 1 dimensional korteweg de vries equation are found by virtue of binary bell polynomials all conserved densities and fluxes are given with explicit recursion formulas

solitons backlund transformation and lax pair for the 2 1 dimensional boiti leon pempinelli equation for the water waves under investigation in this paper is the 2 1 dimensional boiti leon pempinelli blp equation for the water waves by virtue of the binary bell polynomials and symbolic computation the bilinear form for the blp equation is obtained furthermore soliton solutions are presented and soliton interaction properties including the elastic inelastic and elastic inelastic collisions are discussed by the graphical analysis besides the backlund transformation in the form of the binary bell polynomials is derived via the backlund transformation the shock wave solutions and lax pair are both constructed

exponential time decay of solutions to reaction cross diffusion systems of maxwell stefan type the large time asymptotics of weak solutions to maxwell stefan diffusion systems for chemically reacting fluids with different molar masses and reversible reactions are investigated the diffusion matrix of the system is generally neither symmetric nor positive definite but the equations admit a formal gradient flow structure which provides entropy free energy estimates the main result is the exponential decay to the unique equilibrium with a rate that is constructive up to a finite dimensional inequality the key elements of the proof are the existence of a unique detailed balance equilibrium and the derivation of an inequality relating the entropy and the entropy production the main difficulty comes from the fact that the reactions are represented by molar fractions while the conservation laws hold for the concentrations the idea is to enlarge the space of n partial concentrations by adding the total concentration viewed as an independent variable thus working with n 1 variables further results concern the existence of global bounded weak solutions to the parabolic system and an extension of the results to complex balance systems

on modified nls kaup and nlbq equations differential transformations and bilinearization new transformations between the nonlinear schrodinger kaup and non local boussinesq equations as well as their modified counterparts are found and analysed the bilinear representations of these equations including an alternative bilinear form of the chen lee liu equation are obtained by a direct method based on the bell s exponential polynomials explicit wronskian solutions to these equations are also presented

a modified bfgs method and its global convergence in nonconvex minimization in this paper we propose a modification of the bfgs method for unconstrained optimization a remarkable feature of the proposed method is that it possesses a global convergence property even without convexity assumption on the objective function under certain conditions we also establish superlinear convergence of the method

an integrable hierarchy and darboux transformations bilinear backlund transformations of a reduced equation a new integrable hierarchy of evolution equations is obtained by making use of a lie algebra and tu ma scheme from which a new generalized broer kaup gbk equation is produced then two kinds of darboux transformations the bilinear presentation the bilinear backlund transformation and the new lax pair of the gbk equation are generated respectively by employing the bell polynomials

lump solutions of a generalized calogero bogoyavlenskii schiff equation abstract a generalized calogero bogoyavlenskii schiff equation is considered and based on its hirota bilinear form a class of lump solutions is explicitly generated via symbolic computations with maple together with plots of a specific lump solution the result enlarges the category of nonlinear partial differential equations which possess lump solutions

discussion on integrable properties for higher dimensional variable coefficient nonlinear partial differential equations in this paper we introduce two new higher dimensional variable coefficient partial differential equations one is a 2 1 dimensional equation which can be reduced to the well known kp equation which first occurs to the paper b b kadomtsev and v i petviashvili on the stability of solitary waves in weakly dispersive media sov phys dokl 15 539 1970 whose bilinear representation lax pairs backlund transformations and infinite conservation laws are obtained respectively by using the bell polynomials another one is a 3 1 dimensional equation whose integrability is also investigated by us and whose lax pairs backlund transformations and infinite conservation laws are obtained respectively

on the isothermal compressible multi component mixture flow the local existence and maximal lp lq regularity of solutions abstract we consider the initial boundary value problem for the system of equations describing the flow of compressible isothermal mixture of arbitrary large number of components the system consists of the compressible navier stokes equations and a subsystem of diffusion equations for the species the subsystems are coupled by the form of the pressure and the strong cross diffusion effects in the diffusion fluxes of the species assuming the existence of solutions to the symmetrized and linearized equations proven in piasecki shibata and zatorska 2019 we derive the estimates for the nonlinear equations and prove the local in time existence and maximal l p l q regularity of solutions