bright soliton solution to a generalized burgers kdv equation with time dependent coefficients abstract we consider a generalized burgers kdv type equation with time dependent coefficients incorporating a generalized evolution term the effects of third order dispersion dissipation nonlinearity nonlinear diffusion and reaction the exact bright soliton solution for the considered model is obtained by using a solitary wave ansatz in the form of sechs function the physical parameters in the soliton solution are obtained as functions of the time varying coefficients and the dependent exponents the dependent exponents and the temporal variations of the model coefficients satisfy certain parametric conditions as shown by the obtained soliton solution this solution may be useful to explain some physical phenomena in genuinely nonlinear dynamical systems that are described by burgers kdv type models

correction of mismatched l values in bicm receivers in this work we analyze the problem of correction of the reliability metrics l values in bit interleaved coded modulation bicm receivers first we propose a method for finding the linear correction factors that minimize the probability of error of a maximum likelihood decoder that uses the corrected l values to this end we use the efficient approximation of the pairwise error probability in the domain of the cumulant generating functions cgf of the l values and conclude that the optimal correction factors are equal to the twice of value of the saddlepoint of the cgf next a simple extension of the proposed method to the non linear correction is presented we provide numerical examples demonstrating improvements attainable with the proposed method comparing it to the competitive solutions

separatrix crossing time invariant potentials with dissipation strongly nonlinear oscillations in a double well potential that cross a separatrix due to dissipation are analyzed away from the separatrix the nearly periodic oscillations are found using standard asymptotic techniques that are known to fail near the separatrix the solution near the separatrix is represented as a large sequence of perturbed solitary pulses the asymptotic behavior of this sequence is matched forward and backward in time to the nearly periodic oscillations in this manner the oscillations in the post crossing region are connected for the first time to initial conditions in particular we determine the amplitude and the phase of the nonlinear oscillator after crossing the separatrix and show them to be sensitively dependent on the initial conditions the shift between the critical times associated with the slow variation theory before and after crossing the separatrix is derived

interactions of solitons in nonintegrable systems direct perturbation method and applications abstract problems of approximate description of soliton interaction in nonintegrable systems are discussed it is shown that in an arbitrary lagrangian system in the first nontrivial order of the small parameter asymptotic scheme for a system of solitons with close velocities a lagrangian may be introduced analogous to that for classical particles with a pair interaction potential a classification of possible types of soliton interaction is given and criteria of the existence of bound states are formulated a possibility of generalization of approximated description of soliton interaction in the multidimensional case is noted

shape optimal design using b splines abstract shape optimal design of an elastic structure is formulated using a design element technique it is shown that bezier and b spline curves typical of the cad philosophy are well suited to the definition of design elements complex geometries can be described in a very compact way by a small set of design variables and a few design elements because of the b splines flexibility it is no longer necessary to piece design elements together in order to agree with the shape complexity nor to restrict the shape variations moreover the additional optimization constraints that are most often needed to avoid unrealistic designs when the shape variables are the nodal coordinates of a finite element mesh are automatically taken into account in the new formulation an analytical derivation of the sensitivity analysis will be established giving rise to numerical efficiency it will be seen that the resulting optimization problem does not involve highly nonlinear functions with respect to the shape variables so that simple mathematical programming algorithms can be applied to solve it some numerical examples are offered to demonstrate the power and generality of the new approach presented in this paper

on the information loss of the max log approximation in bicm systems we present a comprehensive study of the information rate loss of the max log approximation for m ary pulse amplitude modulation pam in a bit interleaved coded modulation bicm system it is widely assumed that the calculation of l values using the max log approximation leads to an information loss we prove that this assumption is correct for all m pam constellations and labelings with the exception of a symmetric 4 pam constellation labeled with a gray code we also show that for max log l values the bicm generalized mutual information gmi which is an achievable rate for a standard bicm decoder is too pessimistic in particular it is proved that the so called harmonized gmi which can be seen as the sum of bit level gmis is achievable without any modifications to the decoder we then study how bit level channel symmetrization and mixing affect the mi and the gmi for max log l values our results show that these operations which are often used when analyzing bicm systems preserve the gmi however this is not necessarily the case when the mi is considered necessary and sufficient conditions under which these operations preserve the mi are provided

interaction of sine gordon kinks with defects the two bounce resonance a model of soliton defect interactions in the sine gordon equations is studied using singular perturbation theory melnikov theory is used to derive a critical velocity for strong interactions which is shown to be exponentially small for weak defects matched asymptotic expansions for nearly heteroclinic orbits are constructed for the initial value problem which are then used to derive analytical formulas for the locations of the well known two and three bounce resonance windows as well as several other phenomena seen in numerical simulations

a freeform shape optimization of complex structures represented by arbitrary polygonal or polyhedral meshes in this paper we propose a new scheme for freeform shape optimization on arbitrary polygonal or polyhedral meshes the approach consists of three main steps 1 surface partitioning of polygonal meshes into different patches 2 a new freeform perturbation scheme of using the cox de boor basis function over arbitrary polygonal meshes which supports multi resolution shape optimization and does not require cad information 3 freeform shape optimization of arbitrary polygonal or polyhedral meshes numerical experiments indicate the effectiveness of the proposed approach copyright 2004 john wiley sons ltd

a perturbation theory for soliton systems abstract a simplified perturbational approach appropriate for systems of solitons governed by the perturbed integrable equations is described some applications of this method are reviewed among them there are soliton structure of the shock waves in dispersive media double sine gordon equation etc

optimal shape design for thin walled beam cross sections problems of shape optimization for thin walled beam cross sections are investigated in particular shape optimization under torsional loading is treated the shape of the beam cross section is described by non uniform rational b splines nurbs biquadratic and p version finite elements are used to calculate the warping function the definition of the element geometry is carried out by isoparametric and b spline mappings both methods are discussed and compared for structural shape optimization the b spline mapping in connection with the p version finite elements is very efficient the optimization is implemented using convex linearisation and a dual method of mathematical programming sensitivity analysis is performed analytically sample calculations are included

structural shape optimization for the torsion problem using direct integration and b splines abstract a method to optimize the cross sectional shape of a prismatic bar under saint venant s torsion using direct integration of the integral equations is developed the problems of torsional rigidity maximization and mass minimization are handled the shape of the cross section is described by b spline curves the optimization is carried out by a dual method of mathematical programming direct differentiation of the equations is used for the sensitivity analysis numerical examples demonstrate the application of the algorithm

a universal separatrix map for weak interactions of solitary waves in generalized nonlinear schrodinger equations abstract it is known that weak interactions of two solitary waves in generalized nonlinear schrodinger nls equations exhibit fractal dependence on initial conditions and the dynamics of these interactions is governed by a universal two degree of freedom ode system y zhu j yang universal fractal structures in the weak interaction of solitary waves in generalized nonlinear schrodinger equations phys rev e 75 2007 036605 in this paper this ode system is analyzed comprehensively using asymptotic methods along separatrix orbits a simple second order map is derived this map does not have any free parameters after variable rescalings and thus is universal for all weak interactions of solitary waves in generalized nls equations comparison between this map s predictions and direct simulations of the ode system shows that the map can capture the fractal scattering phenomenon of the ode system very well both qualitatively and quantitatively

asymptotic solitons for a higher order modified korteweg de vries equation solitary wave interaction for a higher order modified korteweg de vries mkdv equation is examined the higher order mkdv equation can be asymptotically transformed to the mkdv equation if the higher order coefficients satisfy a certain algebraic relationship the transformation is used to derive the higher order two soliton solution and it is shown that the interaction is asymptotically elastic moreover the higher order phase shifts are derived using the asymptotic theory numerical simulations of the interaction of two higher order solitary waves are also performed two examples are considered one satisfies the algebraic relationship derived from the asymptotic theory and the other does not for the example which satisfies the algebraic relationship the numerical results confirm that the collision is elastic the numerical and theoretical predictions for the higher order phase shifts are also in strong agreement for the example which does not satisfy the algebraic relationship the numerical results show that the collision is inelastic an oscillatory wavetrain is produced by the interacting solitary waves also the higher order phase shifts for this inelastic example are tabulated for a range of solitary wave amplitudes an asymptotic mass conservation law is derived and used to test the finite difference scheme for the numerical solutions it is shown that in general mass is not conserved by the higher order mkdv equation but varies during the interaction of the solitary waves

distribution of max log metrics for qam based bicm in fading channels in this letter we derive closed form expressions for the probability density functions pdfs of the bits reliability metrics l values in bit interleaved coded modulation bicm transmission over fully interleaved fading channels the expressions are valid for the relevant case of quadrature amplitude modulation qam with gray mapping when the metrics are calculated via the so called max log approximation using the developed expressions the performance of coded bicm transmissions is efficiently evaluated i e without resorting to otherwise required two dimensional numerical integration the bicm capacity for different fading channels and constellation sizes is also evaluated

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

bit interleaved coded modulation revisited a mismatched decoding perspective we revisit the information theoretic analysis of bit interleaved coded modulation bicm by modeling the bicm decoder as a mismatched decoder the mismatched decoding model is well defined for finite yet arbitrary block lengths and naturally captures the channel memory among the bits belonging to the same symbol we give two independent proofs of the achievability of the bicm capacity calculated by caire et al where bicm was modeled as a set of independent parallel binary input channels whose output is the bitwise log likelihood ratio our first achievability proof uses typical sequences and shows that due to the random coding construction the interleaver is not required the second proof is based on the random coding error exponents with mismatched decoding where the largest achievable rate is the generalized mutual information moreover the generalized mutual information of the mismatched decoder coincides with the infinite interleaver bicm capacity we show that the error exponent and hence the cutoff rate of the bicm mismatched decoder is upper bounded by that of coded modulation and may thus be lower than in the infinite interleaved model for binary reflected gray mapping in gaussian channels the loss in error exponent is small we also consider the mutual information appearing in the analysis of iterative decoding of bicm with extrinsic information transfer exit charts if the symbol metric has knowledge of the transmitted symbol exit mutual information admits a representation as a pseudo generalized mutual information which is in general not achievable a different symbol decoding metric for which the extrinsic side information refers to the hypothesized symbol induces a generalized mutual information lower than the coded modulation capacity in this case perfect extrinsic side information turns the mismatched decoder error exponent into that of coded modulation

breakup of a multisoliton state of the linearly damped nonlinear schrodinger equation we address the breakup splitting of multisoliton solutions of the nonlinear schrodinger equation nlse occurring due to linear loss two different approaches are used for the study of the splitting process the first one is based on the direct numerical solution of the linearly damped nlse and the subsequent analysis of the eigenvalue drift for the associated zakharov shabat spectral problem the second one involves the multisoliton adiabatic perturbation theory applied for studying the evolution of the solution parameters with the linear loss taken as a small perturbation we demonstrate that in the case of strong nonadiabatic loss the evolution of the zakharov shabat eigenvalues can be quite nontrivial we also demonstrate that the multisoliton breakup can be correctly described within the framework of the adiabatic perturbation theory and can take place even due to small linear loss eventually we elucidate the occurrence of the splitting and its dependence on the phase mismatch between the solitons forming a two soliton bound state

shape design for thin walled beam cross sections using rational b splines shape optimization of thin walled beams is discussed the cross sectional shape of the beam is described by nonuniform rational b spline curves the optimization problem is defined in terms of cross sectional properties and stresses design variables are the control parameters of the rational b spline curves and the wall thickness of the beam cross sectional properties and stresses are obtained from the elasticity solution for the beam consideration of torsion and pure shear requires the solution of laplace equations which is accomplished using finite elements a design sensitivity analysis is given for the cross sectional properties and stresses a sample problem is presented to illustrate the formulations

bit interleaved coded modulation with mismatched decoding metrics bit interleaved coded modulation bicm has become the de facto coding standard for communication systems recently bicm has been cast as a mismatched decoding scheme due to the assumption of independent bit metrics in addition to this inherent mismatch practical demodulators may produce mismatched decoding metrics because of implementation constraints such as clipping and metric approximation to reduce computational complexity in this paper we investigate bicm with such metrics in line with recent works on this topic we adopt the generalized mutual information gmi as the pertinent performance measure first we show that level dependent scaling of logarithmic bit metrics can improve the bicm gmi second we propose a uniform metric scaling which can lead to an improved performance of mismatched sum product symbol by symbol decoding even if the gmi is not changed third we investigate general metric mismatch correction methods and analyze their effects in terms of the gmi by means of three application examples we illustrate that metric mismatch correction including metric scaling can significantly increase bicm rates

computational method for optimization of structural shapes in the direct method of shape optimum design mesh regridding is a necessary step in avoiding the distortion of finite element grids the effect of internal nodal movements on the shape design sensitivity associated with the regridding process has been carefully examined in this paper it shows that to maintain computational accuracy the effects of internal nodal movement should be considered in shape design sensitivity analysis to take the internal nodal movement into account the numerical accuracy of the speed method is investigated a new approach which constructs the velocity field over the element domain is presented although it takes more computational time the new approach does improve the accuracy of shape design sensitivity

mismatched decoding revisited general alphabets channels with memory and the wide band limit the mismatch capacity of a channel is the highest rate at which reliable communication is possible over the channel with a given possibly suboptimal decoding rule this quantity has been studied extensively for single letter decoding rules over discrete memoryless channels dmcs here we extend the study to memoryless channels with general alphabets and to channels with memory with possibly non single letter decoding rules we also study the wide band limit and in particular the mismatch capacity per unit cost and the achievable rates on an additive noise spread spectrum system with single letter decoding and binary signaling

universal fractal structures in the weak interaction of solitary waves in generalized nonlinear schrodinger equations weak interactions of solitary waves in the generalized nonlinear schr odinger equations are studied it is first shown that these interactions exhibit similar fractal dependence on initial conditions for different nonlinearities then by using the karpman solov ev method a universal system of dynamical equations is derived for the velocities amplitudes positions and phases of interacting solitary waves these dynamical equations contain a single parameter which accounts for the different forms of nonlinearity when this parameter is zero these dynamical equations are integrable and the exact analytical solutions are derived when this parameter is nonzero the dynamical equations exhibit fractal structures which match those in the original wave equations both qualitatively and quantitatively thus the universal nature of fractal structures in the weak interaction of solitary waves is analytically established the origin of these fractal structures is also explored it is shown that these structures bifurcate from the initial conditions where the solutions of the integrable dynamical equations develop finite time singularities based on this observation an analytical criterion for the existence and locations of fractal structures is obtained lastly these analytical results are applied to the generalized nonlinear schr odinger equations with various nonlinearities such as the saturable nonlinearity and predictions on their weak interactions of solitary waves are made

adiabatic interaction of n ultrashort solitons universality of the complex toda chain model using the karpman solov ev method we derive the equations for the two soliton adiabatic interaction for solitons of the modified nonlinear schrodinger equation mnse then we generalize these equations to the case of n interacting solitons with almost equal velocities and widths on the basis of this result we prove that the n mnse soliton train interaction n 2 can be modeled by the completely integrable complex toda chain ctc this is an argument in favor of universality of the complex toda chain that was previously shown to model the soliton train interaction for nonlinear schrodinger solitons the integrability of the ctc is used to describe all possible dynamical regimes of the n soliton trains that include asymptotically free propagation of all n solitons n soliton bound states various mixed regimes etc it allows also to describe analytically the manifolds in the 4n dimensional space of initial soliton parameters that are responsible for each of the regimes mentioned above we compare the results of the ctc model with the numerical solutions of the mnse for two and three soliton interactions and find a very good agreement

a perturbational approach to the two soliton systems abstract the two soliton systems of the perturbed non linear schrodinger nls and sine gordon sg equations are considered by means of a simple quasi particle approach in which the soliton interaction and the action of an external perturbation are described by the one soliton perturbation theory the method is quite general it does not assume the knowledge of the exact unperturbed multi soliton solutions it is restricted however by the requirement that the distances between the solitons must be large enough the validity of the approach is checked by applying it to some cases where it is possible to make a comparison with the inverse scattering method different types of soliton collisions and bound soliton systems are investigated in particular detailed descriptions of the two soliton systems of the double sg equations are presented

an approximation concepts approach to shape optimal design abstract in the past much of the work done in structural optimization consisted in resizing the members of fixed configuration models in that case a powerful design procedure has now emerged which is based on the coordinate use of explicit high quality approximations of the behavior constraints and dual methods of mathematical programming there is however a large class of problems for which the main degrees of freedom for the designer correspond to the shape of the structure itself the main objectives of this paper are to recall briefly a convenient geometric representation in which the boundaries of the structure are represented by bezier or b spline curves and then to discuss the choice of optimization algorithm it is shown that cost efficient methods for structural sizing may be advantageously extended to shape optimal design problems different approximation schemes are tested and a new general optimization algorithm is presented that combines mixed approximations and dual methods many large scale applications are treated to demonstrate the generality and the efficiency of the new formulation finally considerations are given about an integrated approach including cad computer codes and finite element optimization software

kink antikink interactions in a modified sine gordon model we study numerically the interactions of a kink k and an antikink k in a parametrically modified sine gordon model with potential v 1 r 2 1 cos 1 r2 2rcos as the parameter r is varied from the pure sine gordon case r 0 to values for which the model is not completely integrable r 0 we find that a rich structure arises in the kk collisions for some regions of r 0 20 r 0 this structure is very similar to that observed in kk interactions in the 4 model and we show that the theory recently suggested for these collisions also applies quantitatively to the modified sine gordon model in other regions of r we observe new scattering phenomena which we present in detail numerically and discuss in a qualitative manner analytically

capacity approaching bandwidth efficient coded modulation schemes based on low density parity check codes we design multilevel coding mlc and bit interleaved coded modulation bicm schemes based on low density parity check ldpc codes the analysis and optimization of the ldpc component codes for the mlc and bicm schemes are complicated because in general the equivalent binary input component channels are not necessarily symmetric to overcome this obstacle we deploy two different approaches one based on independent and identically distributed i i d channel adapters and the other based on coset codes by incorporating i i d channel adapters we can force the symmetry of each binary input component channel by considering coset codes we extend the concentration theorem based on previous work by richardson et al see ibid vol 47 p 599 618 feb 2001 and kavc spl caron ic spl acute et al see ibid vol 49 p 1636 52 july 2003 we also discuss the relation between the systems based on the two approaches and show that they indeed have the same expected decoder behavior next we jointly optimize the code rates and degree distribution pairs of the ldpc component codes for the mlc scheme the optimized irregular ldpc codes at each level of mlc with multistage decoding msd are able to perform well at signal to noise ratios snr very close to the capacity of the additive white gaussian noise awgn channel we also show that the optimized bicm scheme can approach the parallel independent decoding pid capacity as closely as does the mlc pid scheme simulations with very large codeword length verify the accuracy of the analytical results finally we compare the simulated performance of these coded modulation schemes at finite codeword lengths and consider the results from the perspective of a random coding exponent analysis

on the optimality of the binary reflected gray code this paper concerns the problem of selecting a binary labeling for the signal constellation in m psk m pam and m qam communication systems gray labelings are discussed and the original work by frank gray is analyzed as is noted the number of distinct gray labelings that result in different bit error probability grows rapidly with increasing constellation size by introducing a recursive gray labeling construction method called expansion the paper answers the natural question of what labeling among all possible constellation labelings will give the lowest possible average probability of bit errors for the considered constellations under certain assumptions on the channel the answer is that the labeling proposed by gray the binary reflected gray code is the optimal labeling for all three constellations which has surprisingly never been proved before

vector soliton collision dynamics in nonlinear optical fibers we consider the interactions of two identical orthogonally polarized vector solitons in a nonlinear optical fiber with two polarization directions described by a coupled pair of nonlinear schrodinger equations we study a low dimensional model system of hamiltonian ordinary differential equations odes derived by ueda and kath and also studied by tan and yang we derive a further simplified model which has similar dynamics but is more amenable to analysis sufficiently fast solitons move by each other without much interaction but below a critical velocity the solitons may be captured in certain bands of initial velocities the solitons are initially captured but separate after passing each other twice a phenomenon known as the two bounce or two pass resonance we derive an analytic formula for the critical velocity using matched asymptotic expansions for separatrix crossing we determine the location of these resonance windows numerical simulations of the ode models show they compare quite well with the asymptotic theory

complexity and regularity of vector soliton collisions in this paper we extensively investigate the collision of vector solitons in the coupled nonlinear schrodinger equations first we show that for collisions of orthogonally polarized and equal amplitude vector solitons when the cross phase modulational coefficientb is small a sequence of reflection windows similar to that in the f 4 model arises when b increases a fractal structure unlike f 4 s gradually emerges but when b is greater than one this fractal structure disappears analytically we explain these collision behaviors by a variational model that qualitatively reproduces the main features of these collisions this variational model helps to establish that these window sequences and fractal structures are caused entirely or partially by a resonance mechanism between the translational motion and width oscillations of vector solitons next we investigate collision dependence on initial polarizations of vector solitons we discovered a sequence of reflection windows that is phase induced rather than resonance induced analytically we have derived a simple formula for the locations of these phase induced windows and this formula agrees well with the numerical data last we discuss collision dependence on relative amplitudes of initial vector solitons we show that when vector solitons have different amplitudes the collision structure simplifies feasibility of experimental obser vation of these results is also discussed at the end of the paper

survey of shape parameterization techniques for high fidelity multidisciplinary shape optimization a survey is provided of shape parameterization techniques formultidisciplinary optimization and some emerging ideas are highlighted the survey focuses on the suitability of available techniques for multidisciplinary applications of complex cone gurations using high e delity analysis tools such as computational e uid dynamics and computational structural mechanics the suitability criteria are based on the efe ciency effectiveness ease of implementation and availability of analytical sensitivities for geometry and grids a section on sensitivity analysis grid regeneration and grid deformation techniques is also provided