integrable nonlocal wave interaction models the equations we investigate describe the nonlinear and nonlocal interaction of waves in 1 1 dimensions with potential applicability although these equations are integrable the solution of the initial and boundary value problem requires a judicious use of spectral methods in particular we show that spectral data evolve linearly only for special boundary values

otoacoustic emissions from normal hearing and hearing impaired subjects distortion product responses distortion product otoacoustic emissions dpoae were measured in normal hearing and hearing impaired human subjects analyses based on decision theory were used to evaluate dpoae test performance specifically relative operating characteristic roc curves were constructed and the areas under these curves were used to estimate the extent to which normal and impaired ears could be correctly identified by these measures dpoae amplitude and dpoae noise measurements were able to distinguish between normal and impaired subjects at 4000 8000 and to a lesser extent at 2000 hz the ability of these measures to distinguish between groups decreased however as frequency and audiometric criterion used to separate normal and hearing impaired ears decreased at 500 hz performance was no better than chance regardless of the audiometric criterion for normal hearing cumulative distributions of misses hearing impaired ears incorrectly identified as normal hearing and false alarms normal hearing ears identified as hearing impaired were constructed and used to evaluate test performance for a range of hit rates i e the percentage of correctly identified hearing impaired ears depending on the desired hit rate criterion values of 5 to 12 db spl for dpoae amplitudes and 8 to 15 db for dpoae noise accurately distinguished normal hearing ears from those with thresholds greater than 20 db hl for the two frequencies at which performance was best 4000 and 8000 hz it would appear that dpoae measurements can be used to accurately identify the presence of high frequency hearing loss but are not accurate predictors of hearing status at lower frequencies at least for the conditions of the present measurements

subspace clustering of categorical and numerical data with an unknown number of clusters in clustering analysis data attributes may have different contributions to the detection of various clusters to solve this problem the subspace clustering technique has been developed which aims at grouping the data objects into clusters based on the subsets of attributes rather than the entire data space however the most existing subspace clustering methods are only applicable to either numerical or categorical data but not both this paper therefore studies the soft subspace clustering of data with both of the numerical and categorical attributes also simply called mixed data for short specifically an attribute weighted clustering model based on the definition of object cluster similarity is presented accordingly a unified weighting scheme for the numerical and categorical attributes is proposed which quantifies the attribute to cluster contribution by taking into account both of intercluster difference and intracluster similarity moreover a rival penalized competitive learning mechanism is further introduced into the proposed soft subspace clustering algorithm so that the subspace cluster structure as well as the most appropriate number of clusters can be learned simultaneously in a single learning paradigm in addition an initialization oriented method is also presented which can effectively improve the stability and accuracy of k means type clustering methods on numerical categorical and mixed data the experimental results on different benchmark data sets show the efficacy of the proposed approach

support vector data descriptions and k means clustering one class we present clustersvdd a methodology that unifies support vector data descriptions svdds and k means clustering into a single formulation this allows both methods to benefit from one another i e by adding flexibility using multiple spheres for svdds and increasing anomaly resistance and flexibility through kernels to k means in particular our approach leads to a new interpretation of k means as a regularized mode seeking algorithm the unifying formulation further allows for deriving new algorithms by transferring knowledge from one class learning settings to clustering settings and vice versa as a showcase we derive a clustering method for structured data based on a one class learning scenario additionally our formulation can be solved via a particularly simple optimization scheme we evaluate our approach empirically to highlight some of the proposed benefits on artificially generated data as well as on real world problems and provide a python software package comprising various implementations of primal and dual svdd as well as our proposed clustersvdd

improved multi kernel classification machine with nystrom approximation technique kernelized modification of ho kashyap algorithm with squared approximation of the misclassification errors kmhks is an effective algorithm for nonlinearly separable classification problems while kmhks only adopts one kernel function so a multi kernel classification machine with reduced complexity named nystrom approximation matrix with multiple kmhkss nmkmhks has been developed but nmkmhks has to initialize many parameters and has not an ability to deal with noise well to this end we propose an improved multi kernel classification machine with nystrom approximation technique inmkmhks inmkmhks is based on a new way of generating kernel functions and a new nystrom approximation technique the contributions of inmkmhks are that 1 avoiding the problem of setting too many parameters 2 keeping comparable space and computational complexities after comparing with nmkmhks 3 having a tighter generalization risk bound in terms of rademacher complexity analysis 4 having a better recognition than nmkmhks on average 5 possessing an ability to deal with noise and practical images highlightsavoiding the problem of setting some initial parameters keeping a comparable space and computational complexities having a tighter generalization risk bound having a better recognition than nmkmhks on average possessing an ability to deal with noise and practical images

further assessment of forward pressure level for in situ calibration quantifying ear canal sound level in forward pressure has been suggested as a more accurate and practical alternative to sound pressure level spl calibrations used in clinical settings the mathematical isolation of forward and reverse pressure requires defining the thevenin equivalent impedance and pressure of the sound source and characteristic impedance of the load however the extent to which inaccuracies in characterizing the source and or load impact forward pressure level fpl calibrations has not been specifically evaluated this study examined how commercially available probe tips and estimates of characteristic impedance impact the calculation of forward and reverse pressure in a number of test cavities with dimensions chosen to reflect human ear canal dimensions results demonstrate that fpl calibration which has already been shown to be more accurate than in situ spl calibration can be improved particularly around standing wave null frequencies by refining estimates of characteristic i

the global kernel k means algorithm for clustering in feature space kernel k means is an extension of the standard k means clustering algorithm that identifies nonlinearly separable clusters in order to overcome the cluster initialization problem associated with this method we propose the global kernel k means algorithm a deterministic and incremental approach to kernel based clustering our method adds one cluster at each stage through a global search procedure consisting of several executions of kernel k means from suitable initializations this algorithm does not depend on cluster initialization identifies nonlinearly separable clusters and due to its incremental nature and search procedure locates near optimal solutions avoiding poor local minima furthermore two modifications are developed to reduce the computational cost that do not significantly affect the solution quality the proposed methods are extended to handle weighted data points which enables their application to graph partitioning we experiment with several data sets and the proposed approach compares favorably to kernel k means with random restarts

relation of distortion product otoacoustic emission input output functions to loudness the aim of this study is to further explore the relationship between distortion product otoacoustic emission dpoae measurements and categorical loudness scaling cls measurements using multiple linear regression mlr analysis recently thorson et al j acoust soc am 131 1282 1295 2012 obtained predictions of cls loudness ratings from dpoae input output i o functions using mlr analysis the present study extends that work by 1 considering two different and potentially improved mlr models one for predicting loudness rating at specified input level and the other for predicting the input level for each loudness category and 2 validating the new models predictions using an independent set of data strong correlations were obtained between predicted and measured data during the validation process with overall root mean square errors in the range 10 43 16 78 db for the prediction of cls input level supporting the view that dpoae i o measurements can predict cls loudness ratings and input levels and thus may be useful for fitting hearing aids

reliability of distortion product otoacoustic emissions and their relation to loudness the reliability of distortion product otoacoustic emission dpoae measurements and their relation to loudness measurements was examined in 16 normal hearing subjects and 58 subjects with hearing loss the level of the distortion product l d was compared across two sessions and resulted in correlations that exceeded 0 90 the reliability of dpoaes was less when parameters from nonlinear fits to the input output i o functions were compared across visits next the relationship between dpoae i o parameters and the slope of the low level portion of the categorical loudness scaling cls function soft slope was assessed correlations of 0 65 0 74 and 0 81 at 1 2 and 4 khz were observed between cls soft slope and combined dpoae parameters behavioral threshold had correlations of 0 82 0 83 and 0 88 at 1 2 and 4 khz with cls soft slope combining dpoaes and behavioral threshold provided little additional information lastly a multivariate approach utilizing the entire dpoae i o function was used to predict the cls rating for each input level db spl standard error of the estimate when using this method ranged from 2 4 to 3 0 categorical units cu suggesting that dpoae i o functions can predict cls measures within the cu step size used in this study 5

competitive em algorithm for finite mixture models abstract in this paper we present a novel competitive em cem algorithm for finite mixture models to overcome the two main drawbacks of the em algorithm often getting trapped at local maxima and sometimes converging to the boundary of the parameter space the proposed algorithm is capable of automatically choosing the clustering number and selecting the split or merge operations efficiently based on the new competitive mechanism we propose it is insensitive to the initial configuration of the mixture component number and model parameters experiments on synthetic data show that our algorithm has very promising performance for the parameter estimation of mixture models the algorithm is also applied to the structure analysis of complicated chinese characters the results show that the proposed algorithm performs much better than previous methods with slightly heavier computation burden

a discrete linearizability test based on multiscale analysis in this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad graph by the multiple scale reduction around their harmonic solution we show that the a1 a2 and a3 linearizability conditions restrain the number of the parameters which enter into the equation a subclass of the equations which pass the a3 c integrability conditions can be linearized by a mobius transformation

multicomponent integrable wave equations ii soliton solutions the darboux dressing transformations developed in degasperis and lombardo 2007 j phys a math theor 40 961 77 are here applied to construct soliton solutions for a class of boomeronic type equations the vacuum i e vanishing solution and the generic plane wave solution are both dressed to yield one soliton solutions the formulae are specialized to the particularly interesting case of the resonant interaction of three waves a well known model which is of boomeronic type for this equation a novel solution which describes three locked dark pulses simulton is introduced

exact solutions of the 3 wave resonant interaction equation the darboux dressing transformations are applied to the lax pair associated to the system of nonlinear equations describing the resonant interaction of three waves in 1 1 dimensions we display explicit solutions featuring localized waves whose profile vanishes at the spacial boundary x and which are not pure soliton solutions these solutions depend on an arbitrary function and allow us to deal with collisions of waves with various profiles

integrable models in nonlinear optics and soliton solutions nonlinear optics more than other subjects has surprisingly produced quite a number of approximate models which are integrable here we briefly mention these models with the aim of showing contacts between the mathematical and applicative sides of the theory of integrable dynamical systems in particular we illustrate the recent impact of boomeronic type wave equations on applicative issues in the special context of the resonant interaction of three waves

a survey of kernel and spectral methods for clustering clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines the focus of this paper is the partitioning clustering problem with a special interest in two recent approaches kernel and spectral methods the aim of this paper is to present a survey of kernel and spectral clustering methods two approaches able to produce nonlinear separating hypersurfaces between clusters the presented kernel clustering methods are the kernel version of many classical clustering algorithms e g k means som and neural gas spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized an explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation besides fuzzy kernel clustering methods are presented as extensions of kernel k means clustering algorithm

latency of tone burst evoked auditory brain stem responses and otoacoustic emissions level frequency and rise time effects simultaneous measurement of auditory brain stem response abr and otoacoustic emission oae delays may provide insights into effects of level frequency and stimulus rise time on cochlear delay tone burst evoked abrs and oaes tboaes were measured simultaneously in normal hearing human subjects stimuli included a wide range of frequencies 0 5 8 khz levels 20 90 db spl and tone burst rise times abr latencies have orderly dependence on these three parameters similar to previously reported data by gorga et al j speech hear res 31 87 97 1988 level dependence of abr and tboae latencies was similar across a wide range of stimulus conditions at mid frequencies frequency dependence of abr and tboae latencies were similar the dependence of abr latency on both rise time and level was significant however the interaction was not significant suggesting independent effects comparison between abr and tboae latencies reveals that the ratio of tboae latency to abr forward latency the level dependent component of abr total latency is close to one below 1 5 khz but greater than two above 1 5 khz despite the fact that the current experiment was designed to test compatibility with models of reverse wave propagation existing models do not completely explain the current data

cooperative and penalized competitive learning with application to kernel based clustering abstract competitive learning approaches with individual penalization or cooperation mechanisms have the attractive ability of automatic cluster number selection in unsupervised data clustering in this paper we further study these two mechanisms and propose a novel learning algorithm called cooperative and penalized competitive learning cpcl which implements the cooperation and penalization mechanisms simultaneously in a single competitive learning process the integration of these two different kinds of competition mechanisms enables the cpcl to locate the cluster centers more quickly and be insensitive to the number of seed points and their initial positions additionally to handle nonlinearly separable clusters we further introduce the proposed competition mechanism into kernel clustering framework correspondingly a new kernel based competitive learning algorithm which can conduct nonlinear partition without knowing the true cluster number is presented the promising experimental results on real data sets demonstrate the superiority of the proposed methods

integrability of nonlinear wave equations and solvability of their initial value problem we investigate one particular prototypical system of evolution equations in 1 1 dimensions which models the nonlocal interaction of two waves in quadratic nonlinear media these equations are integrable as they possess a lax pair we consider the spectral method of solving the associated initial value problem and as recently pointed out we show that generically the associated initial value problem cannot be linearized we further elaborate on the integrability issue for this model by displaying the corresponding conservation laws and the motion of a particular soliton

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

extended multilinear variable separation approach and multivalued localized excitations for some 2 1 dimensional integrable systems the multilinear variable separation approach and the related universal formula have been applied to many 2 1 dimensional nonlinear systems starting from the universal formula abundant 2 1 dimensional localized excitations have been found in this paper the universal formula is extended in two different ways one is obtained for the modified nizhnik novikov veselov equation such that two universal terms can be combined linearly and this type of extension is also valid for the 2 1 dimensional symmetric sine gordon system the other is for the dispersive long wave equation the broer kaup kupershmidt system the higher order broer kaup kupershmidt system and the burgers system where arbitrary number of variable separated functions can be involved because of the existence of the arbitrary functions in both the original universal formula and its extended forms the multivalued functions can be used to construct a new type of localized excitations folded solitary waves fsws and foldons the fsws

nonlinear schrodinger type equations from multiscale reduction of pdes i systematic derivation in this article we begin a systematic investigation via multiscale expansions of nonlinear evolution pdes partial differential equations in this first article we restrict consideration to a single autonomous but otherwise generic pde in 1 1 variables space time of first order in time whose linear part is dispersive and to solutions dominated by a single plane wave satisfying the linear part of the pde the expansion parameter is an assumedly small coefficient multiplying this plane wave the main indeed asymptotically exact effect of the weak nonlinearity is then to cause a modulation of the amplitude of the plane wave and of its harmonics which is generally described in appropriately defined coarse grained time and space variables by evolution equations of nonlinear schrodinger type a systematic analysis of such equations is presented corresponding to various assumptions on the resonances occurring for the first few harmonics

a two layer mixture model of gaussian process functional regressions and its mcmc em algorithm the mixture of gaussian processes gps is capable of learning any general stochastic process based on a given set of sample curves for the regression and prediction problems however it is ineffective for curve clustering and prediction when the sample curves are derived from different stochastic processes as independent sources linearly mixed together in this paper we propose a two layer mixture model of gp functional regressions gpfrs to describe such a mixture of general stochastic processes or independent sources especially for curve clustering and prediction specifically in the lower layer the mixture of gpfrs mgpfrs is developed for a cluster or class of curves within the input space in the higher layer the mixture of mgpfrs is further established to divide the curves into clusters according to its components in the output space for the parameter estimation of the two layer mixture of gpfrs we develop a monte carlo em algorithm based on a monte carlo markov chain mcmc method in short the mcmc em algorithm we validate the hierarchical mixture of gpfrs and mcmc em algorithm using synthetic and real world data sets our results show that our new model outperforms the conventional mixture models in curve clustering and prediction

estimation of the area function of human ear canals by sound pressure measurements a method to determine the area function of a duct i e the variation of the cross section along the middle axis of the duct is described it is shown that it is sufficient to measure the sound pressure at three locations in the duct to get knowledge of the area function the calculated approximation fits the true area function the better the broader the bandwidth of the sound pressure signals is chosen the bandwidth is bounded by the condition that no higher modes of sound propagation must be excited in principle the area function can be determined by solving a linear system of equations and executing a simple iterative algorithm some more work however is necessary to stabilize the computation against unavoidable small measuring errors the calculated area function reproduces the acoustical transformation characteristics with good precision in spite of this the calculated area function may disagree with the real area function in some regions especially at the edges such errors occur if the deviations of the area function from constant cross section correspond to frequencies outside the range of measurement the method was applied to determine the area function of human ear canals and the results are presented

new integrable pdes of boomeronic type novel integrable systems of coupled first order autonomous pdes in 1 1 dimensions space x and time t are presented integrable covariant 2 vector and 3 vector pdes as well as higher order integrable pdes for a single or a couple of scalar dependent variables including an extension of the sine gordon equation and a remarkably neat highly nonlinear third order pde are also obtained by appropriate reductions of the basic matrix equations the lax pairs that characterize the integrable character of the basic matrix pdes are also exhibited as well as their single soliton solutions these solitons generally exhibit the boomeronic and less generically the trapponic phenomenology namely they do not move uniformly but rather in an appropriate reference system come in from one end in the remote past and boomerang back to that same end in the remote future boomerons or are trapped to oscillate around a value fixed by the initial data trappons

distortion product otoacoustic emission measured with continuously varying stimulus level distortion product otoacoustic emissions dpoae are measured by stimulating the ear with two simultaneous tones a novel method for measuring dpoaes has been developed in which the tone levels vary continuously instead of in discrete steps varying the tone levels continuously may offer advantages for characterizing dpoae level as a function of stimulus level for equivalent primary levels dpoae levels measured with the continuous level method were the same as levels obtained with the discrete level method thus validating the new method continuous level measurements were used to determine the optimal l1 for each l2 in individual subjects n 20 at f2 1 2 4 and 8 khz by using a lissajous path that covered a wide range of stimulus levels the optimal l1 defined as the l1 that resulted in the largest dpoae for each l2 varied across subjects and across frequency the optimal difference between l1 and l2 decreased with increasing l2 at all frequencies and increased with frequency when l2 was low whe

distribution of standing wave errors in real ear sound level measurements standing waves can cause measurement errors when sound pressure level spl measurements are performed in a closed ear canal e g during probe microphone system calibration for distortion product otoacoustic emission dpoae testing alternative calibration methods such as forward pressure level fpl minimize the influence of standing waves by calculating the forward going sound waves separate from the reflections that cause errors previous research compared test performance burke et al 2010 and threshold prediction rogers et al 2010 using spl and multiple fpl calibration conditions and surprisingly found no significant improvements when using fpl relative to spl except at 8 khz the present study examined the calibration data collected by burke et al and rogers et al from 155 human subjects in order to describe the frequency location and magnitude of standing wave pressure minima to see if these errors might explain trends in test performance results indicate that while individual resu

localized excitations in 2 1 dimensional systems by means of a special variable separation approach a common formula with some arbitrary functions has been obtained for some suitable physical quantities of various 2 1 dimensional models such as the davey stewartson ds model the nizhnik novikov veselov nnv system asymmetric nnv equation asymmetric ds equation dispersive long wave equation broer kaup kupershmidt system long wave short wave interaction model maccari system and a general n m component ablowitz kaup newell segur akns system selecting the arbitrary functions appropriately one may obtain abundant stable localized interesting excitations such as the multidromions lumps ring soliton solutions breathers instantons etc it is shown that some types of lower dimensional chaotic patterns such as the chaotic chaotic patterns periodic chaotic patterns chaotic line soliton patterns chaotic dromion patterns fractal lump patterns and fractal dromion patterns may be found in higher dimensional soliton systems the interactions between the traveling ring type soliton solutions are completely elastic the traveling ring solitons pass through each other and preserve their shapes velocities and phases some types of localized weak solutions peakons are also discussed especially the interactions between two peakons are not completely elastic after the interactions the traveling peakons also pass through each other and preserve their velocities and phases however they completely exchange their shapes

the multiscale expansions of difference equations in the small lattice spacing regime and a vicinity and integrability test i we propose an algorithmic procedure i to study the distance between an integrable pde and any discretization of it in the small lattice spacing regime and at the same time ii to test the asymptotic integrability properties of such discretization this method should provide in particular useful and concrete information on how good is any numerical scheme used to integrate a given integrable pde the procedure illustrated on a fairly general ten parameter family of discretizations of the nonlinear schr dinger equation consists of the following three steps i the construction of the continuous multiscale expansion of a generic solution of the discrete system at all orders in following degasperis et al 1997 physica d 100 187 211 ii the application to such an expansion of the degasperis procesi dp integrability test degasperis a and procesi m 1999 asymptotic integrability symmetry and perturbation theory spt98 ed a degasperis and g gaeta singapore world scientific pp 23 37 degasperis a 2001 multiscale expansion and integrability of dispersive wave equations lectures given at the euro summer school what is integrability isaac newton institute cambridge uk 13 24 august integrability lecture notes in physics vol 767 ed a mikhailov berlin springer to test the asymptotic integrability properties of the discrete system and its distance from its continuous limit iii the use of the main output of the dp test to construct infinitely many approximate symmetries and constants of motion of the discrete system through novel and simple formulas

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

influence of primary level and primary frequency ratios on human distortion product otoacoustic emissions the combined influence of primary level differences l1 l2 and primary frequency ratio f2 f1 on distortion product otoacoustic emission dpoae level was investigated in 20 normal hearing subjects dpoaes were recorded with continuously varying stimulus levels neely et al j acoust soc am 117 1248 1259 2005 for the following stimulus conditions f2 1 2 4 and 8 khz and f2 f1 1 05 to 1 4 various l1 l2 including one individually optimized to produce the largest dpoae for broadly spaced primary frequencies at low l2 levels the largest dpoaes were recorded when l1 was much higher than l2 with l1 remaining relatively constant as l2 increased as f2 fl decreased the largest dpoaes were observed when l1 was closer to l2 and increased as l2 increased optimal values for l1 l2 and f2 f1 were derived from these data in general average dpoae levels for the new l1 l2 and f2 f1 were equivalent to or larger than those observed for other stimulus combinations including the l1 l2 described by kummer et al j acoust soc am 103 3431 3444 1998 and those defined by neely et al in which l1 l2 was evaluated but f2 f1 was fixed at 1 2

discrete third order spectral problems and a new toda type equation in this paper we construct the class of equations associated with a discrete spectral problem of third order among the equations of this class we find an integrable differential equation on the lattice with exponential nonlinearity by considering its associated darboux transformation we construct an explicit solution

multiple scale perturbation beyond the nonlinear schroedinger equation i abstract we consider the effect of weak nonlinearity on the propagation of one dimensional strongly dispersive waves in the standard quasi monochromatic approximation it is well known that the first order amplitude modulation satisfies the nonlinear schroedinger equation in slow variables with the assumption that this amplitude modulation has no discrete spectrum component i e no soliton we explore the higher order effects and provide a well defined procedure to compute all coefficients of the perturbative expansion as relatively bounded functions no secularity effects of slow variables the main effect of this procedure is that the leading amplitude modulation satisfies at higher orders the nonlinear schroedinger hierarchy of evolution equations in slow variables key ingredient is the integrability of the nonlinear schroedinger equation and its commuting symmetries

a robust competitive clustering algorithm with applications in computer vision this paper addresses three major issues associated with conventional partitional clustering namely sensitivity to initialization difficulty in determining the number of clusters and sensitivity to noise and outliers the proposed robust competitive agglomeration rca algorithm starts with a large number of clusters to reduce the sensitivity to initialization and determines the actual number of clusters by a process of competitive agglomeration noise immunity is achieved by incorporating concepts from robust statistics into the algorithm rca assigns two different sets of weights for each data point the first set of constrained weights represents degrees of sharing and is used to create a competitive environment and to generate a fuzzy partition of the data set the second set corresponds to robust weights and is used to obtain robust estimates of the cluster prototypes by choosing an appropriate distance measure in the objective function rca can be used to find an unknown number of clusters of various shapes in noisy data sets as well as to fit an unknown number of parametric models simultaneously several examples such as clustering mixture decomposition line plane fitting segmentation of range images and estimation of motion parameters of multiple objects are shown

multicomponent integrable wave equations i darboux dressing transformation the darboux dressing transformations are applied to the lax pair associated with systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both bright and dark soliton solutions the general formalism is set up and the relevant equations are explicitly solved several instances of multicomponent wave equations of applicative interest such as vector nonlinear schrodinger type equations and three resonant wave equations are considered

universal c integrable nonlinear partial differential equation in n 1 dimensions a nonlinear partial differential equation of evolution in n 1 dimensions is exhibited which is c integrable namely integrable via an appropriate change of variables and which also possesses an element of universality as it is obtained by applying a limiting procedure to a class of nonlinear partial differential equations since this limiting procedure corresponds to physical conditions likely to prevail in some phenomenological circumstances it is expected that this equation shall have applicative relevance but this possibility is not pursued in this paper the method whereby this equation has been obtained as well as its integrable character qualify it as a n 1 dimensional analog of the eckhaus equation to which it does indeed reduce for n 1