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007			cr |uu|||uu|||
008			181022s2018 si a ob 001 0 eng d
010			_z 2018043691
040			_aWSPC _beng _cWSPC
020			_a9789813271616 _q(ebook)
020			_z9789813271609 _q(hbk.)
020			_z9813271604 _q(hbk.)
050	0	4	_aQA927 _b.P6595 2018
082	0	4	_a531/.113301515353 _223
100	1		_aPopivanov, Peter R. _920876
245	1	0	_aNonlinear waves _h[electronic resource] : _ba geometrical approach / _cPetar Popivanov, Angela Slavova.
260			_aSingapore : _bWorld Scientific Publishing Co. Pte Ltd., _c©2018.
300			_a1 online resource (208 p.) : _bill. (some col.)
490	0		_aSeries on analysis, applications, and computation ; _vv. 9
538			_aMode of access: World Wide Web.
538			_aSystem requirements: Adobe Acrobat Reader.
588			_aTitle from web page (viewed December 5, 2018).
504			_aIncludes bibliographical references and index.
505	0		_aTraveling waves and their profiles -- Solvability of PDEs from physics and geometry -- Interaction of peakons and kinks -- Dressing method and geometrical applications -- Hirota's method in soliton theory -- Special type solutions of evolution PDEs -- Regularity properties of nonlinear hyperbolic PDEs.
520			_a"This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics. Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used. This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics, quantum mechanics, amongst others."-- _cPublisher's website.
650		0	_aNonlinear wave equations. _911596
650		0	_aNonlinear waves. _93824
650		0	_aMathematical physics. _911013
650		0	_aNonlinear partial differential operators. _920877
650		0	_aElectronic books. _920878
700	1		_aSlavova, Angela. _920879
856	4	0	_uhttps://www.worldscientific.com/worldscibooks/10.1142/11025#t=toc _zAccess to full text is restricted to subscribers.
942			_cEBK
999			_c72664 _d72664