solving the hierarchy of the nonisospectral kdv equation with self consistent sources via the inverse scattering transform the hierarchy of the nonisospectral kdv equation with self consistent sources is derived n soliton solutions of the hierarchy are obtained through the inverse scattering transform we develop new treatment of singularities appearing in the lax pair in the process of determining time revolutions of scattering data our approach is general and can apply to other 1 1 dimensional nonisospectral soliton hierarchy with self consistent sources

integration of the soliton hierarchy with mixed sources abstract we propose a method to find the explicit evolution equation for eigenfunction of the auxiliary linear problems of the soliton hierarchy with mixed sources which consist of both the sum of square of eigenfunctions and integral over the square of eigenfunctions then we determine the evolution equations of scattering data corresponding to the soliton hierarchy with mixed sources and solve the equation in the soliton hierarchy with mixed sources by inverse scattering transformation the new mkdv hierarchy with mixed sources is used as an example to illustrate the method we proposed and the nonlinear schrodinger equation hierarchy with mixed sources the kdv hierarchy with mixed sources are integrated this approach can be applied to all other 1 1 dimensional soliton hierarchies with mixed sources

a generalization of myhill nerode theorem for fuzzy languages the well known myhill nerode theorem provides a necessary and sufficient condition for a language to be regular in the context of fuzzy languages and automata theory myhill nerode type theorems have been proved for fuzzy languages with finite range this paper introduces a new right equivalence relation on the free monoid of an alphabet based on the notion of factorization of fuzzy languages the index of this relation for a fuzzy language with infinite range can be finite this fact allows us to generalize the myhill nerode theorem for any kind of fuzzy languages in this paper is proved that the following two conditions are mutually equivalent for a given fuzzy language x i there exists a factorization such that the right equivalence relation of x defined via the factorization has a finite index ii the fuzzy language x is recognized by a fuzzy deterministic finite automaton

new method for deriving nonlinear integrable systems a new approach is proposed to derive nonlinear integrable systems it is used to obtain several new nonlinear integrable systems the above results are relevant to some problems of hydrodynamics plasma physics solid state physics etc

random number generators in genetic algorithms for unconstrained and constrained optimization abstract presented here is a genetic algorithm that computes an approximate solution to constrained and unconstrained global optimization problems this technique has been implemented using several pseudo and quasi random number generators and the results of several test examples are presented the performance of this technique is based on a ranked comparison of relative error

n soliton solutions for a 2 1 dimensional breaking soliton equation with self consistent sources abstract a 2 1 dimensional breaking soliton equation with self consistent sources 2 1 dbsescs is derived the bilinear form of it is obtained and the n soliton solutions are worked out by means of the hirota method and wronskian technique respectively by making use of the laplace expansion formula a simple method is presented to treat the nonlinear term in the bilinear equation and finish the wronskian verification the dynamics and source effects are investigated

a new multicomponent ckp hierarchy and solutions based on the eigenfunction symmetry constraints we first propose a new multicomponent c type subhierarchy for kadomtsev petviashvili mcckp hierarchy and its lax representation which provides an effective way to find two types of new ckp equation with self consistent sources along with their related lax representations also it admits reductions to k constrained ckp hierarchy and to a 1 1 dimensional soliton hierarchy with self consistent sources which gives rise to two types of new kaup kuperschmidt kk equation with self consistent sources and two types of new bidirectional kaup kuperschmidt equation with self consistent sources by using the solutions of the ckp and kk equations and their corresponding eigenfunctions n soliton solutions for the first type of ckp self consistent source ckpscs and of kkscs are constructed by means of method of variation in constant respectively

brzozowski type determinization for fuzzy automata abstract in this paper we adapt the well known brzozowski determinization method to fuzzy automata this method gives better results than all previously known methods for determinization of fuzzy automata developed by b lohlavek 4 li and pedrycz 20 ignjatovic et al 15 and jancic et al 18 namely as in the case of ordinary nondeterministic automata brzozowski type determinization of a fuzzy automaton results in a minimal crisp deterministic fuzzy automaton equivalent to the starting fuzzy automaton and we show that there are cases when all previous methods result in infinite automata while brzozowski type determinization results in a finite one the paper deals with fuzzy automata over complete residuated lattices but identical results can also be obtained in a more general context for fuzzy automata over lattice ordered monoids and even for weighted automata over commutative semirings

fuzzy regular languages over finite and infinite words we consider finite automata over semirings and quemirings accepting finite and infinite words respectively we obtain kleene theorems for fuzzy languages consisting of finite and infinite words furthermore we introduce regular fuzzy grammars and linear fuzzy systems and we show that both of them specify the class of recognizable fuzzy languages consisting of finite and infinite words

an extended noncommutative kp hierarchy introducing squared eigenfunctions in the moyal deformed lax equations generates an extended noncommutative kp nckp hierarchy the compatibility equations between the nckp flows and the extended nckp flows and the compatibility equations among the extended nckp flows themselves are constructed the n reductions and the k constraints are analyzed and thus the nckp hierarchy with self consistent sources the constrained nckp hierarchy and the constrained nckp hierarchy with self consistent sources are presented various illustrative examples are worked out together with their lax representations involving pseudodifferential lax operators

solving soliton equations with self consistent sources by method of variation of parameters abstract starting from the solutions of soliton equations and corresponding eigenfunctions obtained by darboux transformation we present a new method to solve soliton equations with self consistent sources sescs based on method of variation of parameters the kdv equation with self consistent sources kdvscs is used as a model to illustrate this new method in addition we apply this method to construct some new solutions of the derivative nonlinear schrodinger equation with self consistent sources dnlsscs such as phase solution dark soliton solution bright soliton solution and breather type solution

fuzzy context free languages part 1 generalized fuzzy context free grammars motivated by aspects of robustness in parsing a context free language we study generalized fuzzy context free grammars these fuzzy context free k grammars provide a general framework to describe correctly as well as erroneously derived sentences by a single generating mechanism they model the situation of making a finite choice out of an infinity of possible grammatical errors during each context free derivation step formally a fuzzy context free k grammar is a fuzzy context free grammar with a countable rather than a finite number of rules satisfying the following condition for each symbol the set containing all right hand sides of rules with left hand side equal to forms a fuzzy language that belongs to a given family k of fuzzy languages we investigate the generating power of fuzzy context free k grammars and we show that under minor assumptions on the parameter k the family of languages generated by fuzzy context free k grammars possesses closure properties very similar to those of the family of ordinary context free languages

a new constrained mkp hierarchy and the generalized darboux transformation for the mkp equation with self consistent sources abstract the mkp equation with self consistent sources mkpescs is treated in the framework of the constrained mkp hierarchy we introduce a new constrained mkp hierarchy which may be viewed as the stationary hierarchy of the mkp hierarchy with self consistent sources this offers a natural way to obtain the lax representation for the mkpescs based on the conjugate lax pairs we construct the generalized darboux transformation with arbitrary functions in time t for the mkpescs which in contrast with the darboux transformation for the mkp equation provides a nonauto backlund transformation between two mkpescss with different degrees the formula for n times repeated generalized darboux transformation is proposed and enables us to find the rational solutions including the lump solutions soliton solutions and the solutions of breather type of the mkpescs

cluster based population initialization for differential evolution frameworks this article proposes a procedure to perform an intelligent initialization for population based algorithms the proposed pre processing procedure namely cluster based population initialization cbpi consists of three consecutive stages at the first stage the individuals belonging to a randomly sampled population undergo two subsequent local search algorithms i e a simple local search that performs moves along the axes and rosenbrock algorithm at the second stage the solutions processed by the two local searches undergo the k means clustering algorithm and are grouped into sets on the basis of their euclidean distance at the third stage the best individuals belonging to each cluster are saved into the initial population of a generic optimization algorithm if the population has not been yet filled the other individuals of the population are sampled within the clusters by using a fitness based probabilistic criterion this three stage procedure implicitly performs an initial screening of the problem features in order to roughly estimate the most interesting regions of the decision space the proposed cbpi has been tested on multiple classical and modern differential evolution variants on a wide array of test problems and dimensionality values as well as on a real world problem the proposed intelligent sampling appears to have a significant impact on the algorithmic functioning as it consistently enhances the performance of the algorithms with which it is integrated

a connection between hh3 and korteweg de vries with one source in the system made of korteweg de vries with one source we first show by applying the painleve test that the two components of the source must have the same potential we then explain the natural introduction of an additional term in the potential of the source equations while preserving the existence of a lax pair this allows us to prove the identity between the traveling wave reduction and one of the three integrable cases of the cubic henon heiles hamiltonian system

quasi random initial population for genetic algorithms the selection of the initial population in a population based heuristic optimizationmethod is important since it affects the search for several iterations and often has an influence on the final solution if no a priori information about the optima is available the initial population is often selected randomly using pseudorandom numbers usually however it is more important that the points are as evenly distributed as possible than that they imitate random points in this paper we study the use of quasi random sequences in the initial population of a genetic algorithm sample points in a quasi random sequence are designed to have good distribution properties here a modified genetic algorithm using quasi random sequences in the initial population is tested by solving a large number of continuous benchmark problems from the literature the numerical results of two implementations of genetic algorithms using different quasi random sequences are compared to those of a traditional implementation using pseudorandom numbers the results obtained are promising

capture and confinement of solitons in nonlinear integrable systems the system describing the interaction of a long wave with a short wave packet on thex y plane is considered the solutions are found to describe a soliton that comes from infinity and then is captured into a conditionally periodical oscillatory regime the solutions are also found that describe a soliton coming from infinity and then decaying into two solitons one goes to infinity and the other is captured into a conditionally periodical oscillatory regime the obtained results are relevant to some problems of hydrodynamics plasma physics solid state physics etc

an extended harry dym hierarchy an extended harry dym hierarchy is constructed by using eigenfunctions and adjoint eigenfunctions of the spectral problems of the harry dym hierarchy associated with the pseudo differential operator l u u0 u1 1 the corresponding lax presentation possesses a self consistent source involving squared eigenfunctions the resulting extended harry dym hierarchy is reduced to the harry dym hierarchy with self consistent sources under the n reduction ln ln 2 and the k constrained harry dym hierarchy under the k constraint lk lk 2 ni 1qi 1ri 2 a few particular examples are computed together with their lax pairs

minimization of fuzzy finite automata abstract in this paper we show that a fuzzy finite automation m 1 has an equivalent minimal fuzzy finite automation m we also show that m can be chsen so that if m 2 is equivalent to m 1 then m is a homomorphic image of m 2

the recognizability of sets of graphs is a robust property once the set of finite graphs is equipped with an algebra structure arising from the definition of operations that generalize the concatenation of words one can define the notion of a recognizable set of graphs in terms of finite congruences applications to the construction of efficient algorithms and to the theory of context free sets of graphs follow naturally the class of recognizable sets depends on the signature of graph operations we consider three signatures related respectively to hyperedge replacement hr context free graph grammars to vertex replacement vr context free graph grammars and to modular decompositions of graphs we compare the corresponding classes of recognizable sets we show that they are robust in the sense that many variants of each signature where in particular operations are defined by quantifier free formulas a quite flexible framework yield the same notions of recognizability we prove that for graphs without large complete bipartite subgraphs hr recognizability and vr recognizability coincide the same combinatorial condition equates hr context free and vr context free sets of graphs inasmuch as possible results are formulated in the more general framework of relational structures

solving the kdv hierarchy with self consistent sources by inverse scattering method abstract the evolution of the eigenfunctions in the lax representation of the kdv hierarchy with self consistent sources possesses singularity by proposing a method to treat the singularity to determine the evolution of scattering data the kdv hierarchy with self consistent sources is integrated by the inverse scattering method the soliton solutions of these equations are obtained it is shown that the insertion of a source may cause the variation of the speed of soliton this approach can be applied to other 1 1 dimensional soliton hierarchies

generalized darboux transformations for the kp equation with self consistent sources the kp equation with self consistent sources kpescs is treated in the framework of the constrained kp equation this offers a natural way to obtain the lax representation for the kpescs based on the conjugate lax pairs we construct the generalized binary darboux transformation with arbitrary functions in time t for the kpescs which in contrast to the binary darboux transformation of the kp equation provides a non auto backlund transformation between two kpescss with different degrees the formula for n times repeated generalized binary darboux transformation is proposed and enables us to find the n soliton solution and lump solution as well as some other solutions of the kpescs

bi hamiltonian structure of jm hierarchy with self consistent sources by taking the space variable x as the evolution parameter and introducing the jacobi ostrogradiski coordinates we present t type hamiltonian description of soliton equations with self consistent sources which have not x type hamiltonian formulation when considering t as evolution parameter the t type miura map generates the second hamiltonian structure for these t type hamiltonian systems the two compatible hamiltonian operators are used to construct a hereditary operator and to obtain new hierarchies of infinite dimensional integrable hamiltonian systems the reduction of these equations with sources gives rise to the constrained flows of soliton equations and their bi hamiltonian structure we use the jaulent miodek hierarchy with self consistent sources to illustrate the method c 1999 elsevier science b v all rights reserved

2d toda lattice equation with self consistent sources casoratian type solutions bilinear backlund transformation and lax pair the two dimensional toda lattice equation with self consistent sources is proposed based on its bilinear forms casoratian type solutions and backlund transformation bt for the bilinear forms are presented starting from the bt a lax pair is derived for the 2d toda lattice with self consistent sources

spectral transform and solitons for generalized coupled bloch systems the spectral transform and backlund transformation for a generalization of the coupled bloch system arising in nonlinear optics are studied the equation is related to a singular dispersion relation and is treated as a representative example of a general method for studying such equations the spectral transform is developed through the formalism the backlund transformation is derived in a very general way and solved to obtain the one soliton and breatherlike solutions the nonlinear superposition formula is also constructed

on closure properties of l valued linear languages abstract in 2001 and 2002 daowen qiu has established a new theory of l valued automata which is based on complete residuated lattices moreover besides the finite automata several other classes of machines grammars and languages have been generalized using the ideas introduced by qiu this paper generalizes the concept of linear grammars and linear languages in this context moreover it presents some operations for l valued languages and some closure properties for the l valued linear languages

fuzzy tree language recognizability a fuzzy tree language with membership grades in an arbitrary set is syntactically recognizable s recognizable if its syntactic algebra is finite the equality problem for such languages is decidable and their syntactic algebra can be effectively constructed provided that they are s recognizable linear but non arbitrary tree homomorphisms preserve s recognizability tree automata whose transitions are weighted over the unit interval and whose behavior is computed with respect to a pair made of a t norm distributive over a t conorm have the syntactic recognition power and thus their equivalence problem is decidable however s recognizability is more powerful when dealing with non distributive pairs of such operations

negaton and positon solutions of the soliton equation with self consistent sources the korteweg de vries kdv equation with self consistent sources kdves is used as a model to illustrate this method we present a generalized binary darboux transformation gbdt with an arbitrary time dependent function for the kdves as well as the formula for n times repeated gbdt this gbdt provides non auto backlund transformation between two kdv equations with different degrees of sources and enables us to construct more general solutions with n arbitrary t dependent functions by taking the special t function we obtain multisoliton multipositon multinegaton multisoliton positon multinegaton positon and multisoliton negaton solutions of the kdves

backlund transformations for the kp and mkp hierarchies with self consistent sources using gauge transformations for the corresponding generating pseudo differential operators ln in terms of eigenfunctions and adjoint eigenfunctions we construct several types of auto backlund transformations for the kp hierarchy with self consistent sources kphscs and mkp hierarchy with self consistent sources mkphscs respectively the backlund transformations from kphscs to mkphscs are also constructed in this way

the exact solutions to a ragnisco tu hierarchy with self consistent sources abstract the ragnisco tu hierarchy with self consistent sources is derived the exact solutions of the hierarchy are obtained via the inverse scattering transform ist an explicit form for a solution of the ragnisco tu equation is presented

algebraic aspects of families of fuzzy languages we study operations on fuzzy languages such as union concatenation kleene intersection with regular fuzzy languages and several kinds of iterated fuzzy substitution then we consider families of fuzzy languages closed under a fixed collection of these operations which results in the concept of full abstract family of fuzzy languages or full affl this algebraic structure is the fuzzy counterpart of the notion of full abstract family of languages that has been encountered frequently in investigating families of crisp i e non fuzzy languages some simpler and more complicated algebraic structures such as full substitution closed affl full super affl full hyper affl will be considered as well in the second part of the paper we focus our attention to full affls closed under iterated parallel fuzzy substitution where the iterating process is prescribed by given crisp control languages proceeding inductively over the family of these control languages yields an infinite sequence of full affl structures with increasingly stronger closure properties

infinite fuzzy computations we consider buchi automata weighted over the fuzzy semiring f 0 1 max min 0 1 a buchi theorem for the class of w recognizable series with coefficients in f i e for behaviors of buchi automata over f is established furthermore we show that an infinitary language is buchi recognizable iff its characteristic series is w recognizable

the bisection method in higher dimensions is the familiar bisection method part of some larger scheme the aim of this paper is to present a natural and useful generalisation of the bisection method to higher dimensions the algorithm preserves the salient features of the bisection method it is simple convergence is assured and linear and it proceeds via a sequence of brackets whose infinite intersection is the set of points desired brackets are unions of similar simplexes an immediate application is to the global minimisation of a lipschitz continuous function defined on a compact subset of euclidean space

the periodic solutions of the discrete modified kdv equation with a self consistent source abstract this work is devoted to the application of inverse spectral problem for integration of the periodic solutions of the discrete modified kdv equation with a self consistent source the effective method of solution of the inverse spectral problem for the discrete linear ablowitz ladik equation is presented

syntactic recognizability of graphs with fuzzy attributes abstract we present a syntactic recognition theory for graphs with fuzzy edges and fuzzy nodes by employing the algebraic structure of magmoids several examples are illustrated and it is proved that the cut of a recognizable set of fuzzy graphs is not always recognizable as a set of crisp graphs the described theory is then applied for the recognition of fuzzy cognitive maps and the recognizability of interesting examples of sets of fuzzy cognitive maps is examined

the deduction of the lax representation for constrained flows from the adjoint representation for x and tn finite dimensional hamiltonian systems obtained from the decompositions of zero curvature equations it is shown that their lax representations can be deduced directly from the adjoint representations of the auxiliary linear problems as a consequence the zero curvature representation for soliton hierarchy with source is presented

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

fuzzy tree automata in this paper we map an arbitrary algebra to a completely distributive lattice and define algebras of fuzzy sets when the algebra is a term algebra we obtain fuzzy tree languages after defining fuzzy equational sets fuzzy rational sets and fuzzy recognizable tree languages we derive a kleene theorem for fuzzy tree languages

integrability of the semi discrete toda equation with self consistent sources a new procedure to construct and solve soliton equations with self consistent sources sescss is applied to the semi discrete toda equation based on its bilinear from bilinear backlund transformation bt for the semi discrete toda escs is presented starting from the bt a lax pair is derived for the semi discrete toda escs

on the two dimensional leznov lattice equation with self consistent sources a two dimensional leznov lattice equation with self consistent sources leznovescs is presented through the source generation procedure starting from the casoratian determinant solution of the two dimensional leznov lattice equation as a result the casoratian determinant solution of the leznovescs is obtained besides we also give the grammian determinant solution of the coupled system in addition the bilinear backlund transformation bt for the leznovescs is given

on the pfaffianized kp equation with self consistent sources abstract a new procedure called source generation is applied to the pfaffianized kp equation as a result the pfaffianized kp equation with self consistent sources escs is obtained this coupled system cannot only be reduced to the pfaffianized kp equation but also reduced to the kp equation with self consistent sources kpescs so the pfaffianized kp escs can be viewed as a pfaffian version of the kpescs which indicates the commutativity of the source generation procedure and pfaffianization

constructing hierarchy of sinh gordon type equations from soliton hierarchy with self consistent source abstract a method for constructing hierarchy of sinh gordon shg type equations from soliton hierarchy with self consistent source is proposed the lax representation for the shg type equation is naturally deduced from that for soliton equation with self consistent sources several new hierarchies of shg type equations are presented

on the recognizability of fuzzy languages ii it is shown that a fuzzy language is recognized by a finite monoid iff it has finitely many right derivatives iff it has finitely many left derivatives finally we show that the behaviors of lukasiewicz automata have the above properties

on the non isospectral kadomtsev petviashvili equation with self consistent sources abstract a new procedure called source generation is applied to construct non isospectral soliton equations with self consistent sources as results the non isospectral kadomtsev petviashvili equation with self consistent sources kpescs and its gramm type determinant solutions are obtained furthermore the non isospectral pfaffianized kp equation with self consistent sources is constructed this coupled system can not only be reduced to the non isospectral pfaffianized kp equation but also reduced to the non isospectral kpescs

on the combination of self organized systems to generate pseudo random numbers cellular automata ca is a self organizing structure with complex behavior which can be used to generating pseudo random numbers pure ca has a simple structure and has no ability to produce long sequences of random numbers but in order to resolve this problem a programmable controllable ca pcca using actuating factor or combination of different self organizing criticality phenomena can be used the purpose of the aforementioned methods is the use of the ca speed while preventing the automata self organizing factor for specific use in generating random numbers in this paper a pcca by using sandpile model is proposed the sandpile model is a complex system that operates at a critical state between chaos and order this state is known as self organized criticality soc and is characterized by displaying invariant scale behavior in the precise case of the sandpile model by randomly and continuously dropping sand grains on top of a two dimensional grid lattice a power law relationship between the frequency and size of sand avalanches is observed the avalanche behavior and the pure ca behavior are combined in a novel method which can be used as the pseudo random number generator prng experimental results show that this generator is able to reach a random behavior from a pseudo chaotic one by combining two self organized systems in addition to independency of the initial state it has been also indicated that the generated numbers are independent and its probability distribution is likely to be uniform accordingly some tests of prngs such as entropy chi square diehard and several basic statistical tests have been performed and all of them have been successfully passed

a modified kdv equation with self consistent sources in non uniform media and soliton dynamics two non isospectral modified kdv equations with self consistent sources are derived which correspond to the time dependent spectral parameter satisfying t and t 3 respectively gauge transformation between the first non isospectral equation corresponding to t and its isospectral counterpart is given from which exact solutions and conservation laws for the non isospectral one are easily listed besides solutions to the two nonisospectral modified kdv equations with self consistent sources are derived by means of the hirota method and the wronskian technique respectively nonisospectral dynamics and source effects including one soliton characteristics in non uniform media two solitons scattering and special behaviours related to sources for example the ghost solitons in the degenerate two soliton case are investigated analytically

new factorization of the kaup newell hierarchy abstract the new factorizations of each equation in the kaup newell kn hierarchy into two commuting x and t n finite dimensional integrable hamiltonian systems fdihs via the higher order potential eigenfunction constraints are presented the integrability commutativity and lax representation for these fdihss are deduced from the adjoint representations of the auxiliary linear problems for the kn hierarchy this approach provides a natural way to study soliton hierarchies with source the zero curvature representation and darboux transformation for the kn hierarchy with source related to eigenfunctions are found

the q deformed mkp hierarchy with self consistent sources wronskian solutions and solitons based on the eigenfunction symmetry constraint of the q deformed modified kp hierarchy a q deformed mkp hierarchy with self consistent sources q mkphscss is constructed the q mkphscss contain two types of q deformed mkp equation with self consistent sources by the combination of the dressing method and the method of variation of constants a generalized dressing approach is proposed to solve the q deformed kp hierarchy with self consistent sources q kphscss using the gauge transformation between the q kphscss and the q mkphscss the q deformed wronskian solutions for the q kphscss and the q mkphscss are obtained the one soliton solutions for the q deformed kp mkp equation with a source are given explicitly

fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids we study fuzzy finite automata in which all fuzzy sets are defined by membership functions whose codomain forms a lattice ordered monoid l for these l fuzzy finite automata l ffa for short we provide necessary and sufficient conditions for the extendability of the state transition function it is shown that nondeterministic l ffa nl ffa for short are more powerful than deterministic l ffa dl ffa for short then we give necessary and sufficient conditions for the simulation of an nl ffa by an equivalent dl ffa next we turn to the closure properties of languages defined by l ffas we establish closure under the regular operations and provide conditions for closure under intersection and reversal in particular we show that the family of fuzzy languages accepted by dl ffas is not closed under kleene closure operation and the family of fuzzy languages accepted by nl ffas is not closed under complement operation furthermore we introduce the notions of l fuzzy regular expressions and give the kleene theorem for nl ffas the description of dl ffas by l fuzzy regular expressions is also given finally we investigate the level structures of l ffas our results provide some insight as to what extend properties of l ffas and their languages depend on the algebraic properties of l

pfaffian solution of a semi discrete bkp type equation and its source generation version the pfaffian solution of a semi discrete bkp type equation is obtained at first then utilizing the source generation procedure this equation with self consistent sources bkpescs is presented and its pfaffian solutions are derived finally a bilinear backlund transformation for the semi discrete bkpescs is given

lump solutions to the kadomtsev petviashvili i equation with a self consistent source abstract based on symbolic computations lump solutions to the kadomtsev petviashvili i kpi equation with a self consistent source kpiescs are constructed by using the hirota bilinear method and an ansatz technique in contrast with lower order lump solutions of the kadomtsev petviashvili kp equation the presented lump solutions to the kpiescs exhibit more diverse nonlinear phenomena the method used here is more natural and simpler

the n soliton solutions for the non isospectral mkdv equation the bilinear form of the non isospectral mkdv equation is given and the exact n soliton solutions are obtained through hirota method and wronskian technique respectively c

solution of an initial boundary value problem for coupled nonlinear waves the authors derive and study a hierarchy of nonlinear coupled evolution equations among which is the coupled korteveg de vries schrodinger equation for which they prove that a mixed initial boundary value problem is solvable they give the method of solution together with the backlund transformation and establish the infinite set of conserved densities they finally discuss the applicability of such equations in plasma physics and hydrodynamics