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Kadomtsev–Petviashvili Equation
In mathematics and physics, the Kadomtsev–Petviashvili equation (often abbreviated as KP equation) is a partial differential equation to describe nonlinear wave motion. Named after Boris Borisovich Kadomtsev and Vladimir Iosifovich Petviashvili, the KP equation is usually written as: :\displaystyle \partial_x(\partial_t u+u \partial_x u+\epsilon^2\partial_u)+\lambda\partial_u=0 where \lambda=\pm 1. The above form shows that the KP equation is a generalization to two spatial dimensions, ''x'' and ''y'', of the one-dimensional Korteweg–de Vries (KdV) equation. To be physically meaningful, the wave propagation direction has to be not-too-far from the ''x'' direction, i.e. with only slow variations of solutions in the ''y'' direction. Like the KdV equation, the KP equation is completely integrable. It can also be solved using the inverse scattering transform much like the nonlinear Schrödinger equation. In 2002, the regularized version of the KP equation, naturally referre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Ile may refer to: * iLe, a Puerto Rican singer * Ile District (other), multiple places * Ilé-Ifẹ̀, an ancient Yoruba city in south-western Nigeria * Interlingue (ISO 639:ile), a planned language * Isoleucine, an amino acid * Another name for Ilargi, the moon in Basque mythology * Historical spelling of Islay, Scottish island and girls' name * Another name for the Ili River in eastern Kazakhstan * ''Ile'', a gender-neutral pronoun in Portuguese See also * ILE (other) Ile may refer to: * iLe, a Puerto Rican singer * Ile District (other), multiple places * Ilé-Ifẹ̀, an ancient Yoruba city in south-western Nigeria * Interlingue (ISO 639:ile), a planned language * Isoleucine, an amino acid * Another ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RIAN Archive 151311 Russian Physicist Boris Kadomtsev
RIA Novosti (russian: РИА Новости), sometimes referred to as RIAN () or RIA (russian: РИА, label=none) is a Russian state-owned domestic news agency. On 9 December 2013 by a decree of Vladimir Putin it was liquidated and its assets and workforce were transferred to the newly created Rossiya Segodnya agency. On 8 April 2014 RIA Novosti was registered as part of the new agency. RIA Novosti is headquartered in Moscow. The chief editor is Anna Gavrilova. Content RIA Novosti was scheduled to be closed down in 2014; starting in March 2014, staff were informed that they had the option of transferring their contracts to Rossiya Segodnya or sign a redundancy contract. On 10 November 2014, Rossiya Segodnya launched the Sputnik multimedia platform as the international replacement of RIA Novosti and Voice of Russia. Within Russia itself, however, Rossiya Segodnya continues to operate its Russian language news service under the name RIA Novosti with its ria.ru website. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doklady Akademii Nauk SSSR
The ''Proceedings of the USSR Academy of Sciences'' (russian: Доклады Академии Наук СССР, ''Doklady Akademii Nauk SSSR'' (''DAN SSSR''), french: Comptes Rendus de l'Académie des Sciences de l'URSS) was a Soviet journal that was dedicated to publishing original, academic research papers in physics, mathematics, chemistry, geology, and biology. It was first published in 1933 and ended in 1992 with volume 322, issue 3. Today, it is continued by ''Doklady Akademii Nauk'' (russian: Доклады Академии Наук), which began publication in 1992. The journal is also known as the ''Proceedings of the Russian Academy of Sciences (RAS)''. ''Doklady'' has had a complicated publication and translation history. A number of translation journals exist which publish selected articles from the original by subject section; these are listed below. History The Russian Academy of Sciences dates from 1724, with a continuous series of variously named publications dat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schottky Problem
In mathematics, the Schottky problem, named after Friedrich Schottky, is a classical question of algebraic geometry, asking for a characterisation of Jacobian varieties amongst abelian varieties. Geometric formulation More precisely, one should consider algebraic curves C of a given genus g, and their Jacobians \operatorname(C). There is a moduli space \mathcal_g of such curves, and a moduli space of abelian varieties, \mathcal_g, of dimension g, which are ''principally polarized''. There is a morphism\operatorname: \mathcal_g \to \mathcal_gwhich on points (geometric points, to be more accurate) takes isomorphism class /math> to operatorname(C)/math>. The content of Torelli's theorem is that \operatorname is injective (again, on points). The Schottky problem asks for a description of the image of \operatorname, denoted \mathcal_g = \operatorname(\mathcal_g). The dimension of \mathcal_g is 3g - 3, for g \geq 2, while the dimension of ''\mathcal_g'' is ''g''(''g'' + 1)/2. This me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Novikov–Veselov Equation
In mathematics, the Novikov–Veselov equation (or Veselov–Novikov equation) is a natural (2+1)-dimensional analogue of the Korteweg–de Vries (KdV) equation. Unlike another (2+1)-dimensional analogue of KdV, the Kadomtsev–Petviashvili equation, it is integrable via the inverse scattering transform for the 2-dimensional stationary Schrödinger equation. Similarly, the Korteweg–de Vries equation is integrable via the inverse scattering transform for the 1-dimensional Schrödinger equation. The equation is named after S.P. Novikov and A.P. Veselov who published it in . Definition The Novikov–Veselov equation is most commonly written as where v = v( x_1, x_2, t ), w = w( x_1, x_2, t ) and the following standard notation of complex analysis is used: \Re is the real part, : \partial_ = \frac ( \partial_ - i \partial_ ), \quad \partial_ = \frac ( \partial_ + i \partial_ ). The function v is generally considered to be real-valued. The function w is an auxiliary f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burgers' Equation
Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas of applied mathematics, such as fluid mechanics, nonlinear acoustics, gas dynamics, and traffic flow. The equation was first introduced by Harry Bateman in 1915 and later studied by Johannes Martinus Burgers in 1948. For a given field u(x,t) and diffusion coefficient (or ''kinematic viscosity'', as in the original fluid mechanical context) \nu, the general form of Burgers' equation (also known as viscous Burgers' equation) in one space dimension is the dissipative system: \frac + u \frac = \nu\frac. When the diffusion term is absent (i.e. \nu=0), Burgers' equation becomes the inviscid Burgers' equation: \frac + u \frac = 0, which is a prototype for conservation equations that can develop discontinuities (shock waves). The previous equation is the ''advective form'' of the Burgers' equation. The ''conservative form'' is found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dispersionless Equation
Dispersionless (or quasi-classical) limits of integrable partial differential equations (PDE) arise in various problems of mathematics and physics and have been intensively studied in recent literature (see e.g. references below). They typically arise when considering slowly modulated long waves of an integrable dispersive PDE system. Examples Dispersionless KP equation The dispersionless Kadomtsev–Petviashvili equation (dKPE), also known (up to an inessential linear change of variables) as the Khokhlov–Zabolotskaya equation, has the form : (u_t+uu_)_x+u_=0,\qquad (1) It arises from the commutation : _1, L_20.\qquad (2) of the following pair of 1-parameter families of vector fields : L_1=\partial_y+\lambda\partial_x-u_x\partial_,\qquad (3a) : L_2=\partial_t+(\lambda^2+u)\partial_x+(-\lambda u_x+u_y)\partial_,\qquad (3b) where \lambda is a spectral parameter. The dKPE is the x-dispersionless limit of the celebrated Kadomtsev–Petviashvili equation, arising when considering ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bose–Einstein Condensate
In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.67 °F). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum mechanical phenomena, particularly wavefunction interference, become apparent macroscopically. A BEC is formed by cooling a gas of extremely low density (about 100,000 times less dense than normal air) to ultra-low temperatures. This state was first predicted, generally, in 1924–1925 by Albert Einstein following and crediting a pioneering paper by Satyendra Nath Bose on the new field now known as quantum statistics. In 1995, the Bose-Einstein condensate was created by Eric Cornell and Carl Wieman of the University of Colorado at Boulder using rubidium atoms; later that year, Wolfgang Ketterle of MIT produc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ferromagnetism
Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials are the familiar metals noticeably attracted to a magnet, a consequence of their large magnetic permeability. Magnetic permeability describes the induced magnetization of a material due to the presence of an ''external'' magnetic field, and it is this temporarily induced magnetization inside a steel plate, for instance, which accounts for its attraction to the permanent magnet. Whether or not that steel plate acquires a permanent magnetization itself, depends not only on the strength of the applied field, but on the so-called coercivity of that material, which varies greatly among ferromagnetic materials. In physics, several different types of material magnetism are distinguished. Ferromagnetism (along with the similar effect ferrimagnetis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth's Gravity
The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantity, whose direction coincides with a plumb bob and strength or magnitude is given by the norm g=\, \mathit\, . In SI units this acceleration is expressed in metres per second squared (in symbols, m/ s2 or m·s−2) or equivalently in newtons per kilogram (N/kg or N·kg−1). Near Earth's surface, the gravity acceleration is approximately , which means that, ignoring the effects of air resistance, the speed of an object falling freely will increase by about per second every second. This quantity is sometimes referred to informally as ''little '' (in contrast, the gravitational constant is referred to as ''big ''). The precise strength of Earth's gravity varies depending on location. The nominal "average" value at Earth's surface, known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to float on a water surface without becoming even partly submerged. At liquid–air interfaces, surface tension results from the greater attraction of liquid molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion). There are two primary mechanisms in play. One is an inward force on the surface molecules causing the liquid to contract. Second is a tangential force parallel to the surface of the liquid. This ''tangential'' force is generally referred to as the surface tension. The net effect is the liquid behaves as if its surface were covered with a stretched elastic membrane. But this analogy must not be taken too far as the tension in an elastic membrane is dependent on the amount of deformation of the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
