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ПРЕДМЕТНЫЙ УКАЗАТЕЛЬ 277
Переменные разделяющие, xiv, 174,
176, 185, 194
Поведение доминантное, 18
Полином Аски–Вильсона, 224
Полиномы Белла, 270
Порядок, 198
— возмущения, 3, 20, 33
— детерминанта, 78
— дискретизации, 198, 217
— дифференциальный, 5, 9
—матрицы,22
— особенности, 148
— пары Лакса, 113, 120
—полюса,59
— рассеяния, 123
— роста, 200, 265
— эллиптический, 74
Посвящение, v
Предел непрерывный, 197, 200, 201,
203, 207, 212, 216, 217, 220, 222, 224
Преобразование
— Беклунда, 95, 124, 131, 134, 143, 144,
150
— — билинейное, 270
— Дарбу, 110, 114–116, 119, 146, 171,
214
— Дарбу (бинарное), 115
— Крама, 110, 116
— Миуры, 131
— аффинное, 246, 249
— бирациональное, 167, 168, 214, 232
— годографа, 83, 84, 98, 100
— дробно-рациональное, 8, 40, 46, 78,
100, 106, 168, 210, 219, 221, 231, 249,
255, 260
— масштабное двойное, 197
— сингулярное
— — дифференциальное частное, 5, 110,
147, 214, 269
— — частное, 119, 123
— сохраняющее слои, 233
Преобразования точечные, 232
Производная
— логарифмическая, 4
— шварциана, 101
Псевдопотенциал, 121, 122, 143, 152,
171
Пси-ряды, 16, 51
Пфаффиан, 268
Расстояние, 52, 53, 73
Редукция, xii, 91
— в переменных бегущей волны, 92,
160
— характеристическая, 92, 164, 171
Результант, 78
Решение
— аналитическое общее, xi, 37, 51, 53,
57, 62–64, 73, 87
— в виде плоской волны, 96, 219
— двухсолитонное, xiii, 140, 154, 159,
269
— классическое, 224, 226, 233, 240, 255
— общее, 7, 16, 91, 227
— односолитонное, 96, 140
— особое, 210, 227
— осциллирующее, 142
—точное,7
— трехсолитонное, 269
— частное, ix, 227
— эллиптическое, 59, 73, 85, 87, 157,
160, 164, 220
Род, 68, 78, 80, 82, 177, 181, 182, 194,
223, 236, 255, 256, 259
Ряды
— Лорана, 12
— Пюизё, 24, 51
Свойство Пенлеве, 9, 228
— дискретное, xiv, 198, 200, 203, 207,
216
— для ОДУ, ix, 1, 12
—дляУЧП,97
— слабое, x, 24, 26, 98, 176
Система
— Дарбу–Хальфена, 85
278 ПРЕДМЕТНЫЙ УКАЗАТЕЛЬ
— Риккати проективная, 37, 69, 114,
122, 152
— гиперэллиптическая, 177, 182
Слияние, 221, 224, 241, 246, 252
Солитон, 96
Соотношение контигуальное, 169, 214
Степень, 7, 198, 205, 264
Суммирование повторное, 3, 103
Теорема Бьянки о перестановочности,
119
Теория Неванлинны, 200
Тест Пенлеве, 228
— дискретный, 198, 201
— для ОДУ, ix, 12
— для УЧП, 100
— слабый, x, 24
Тип Фукса, 19
Точка
— ветвления, x
— критическая, x
— разветвления, x
УЧП второго порядка
— гиперболическое, 239
— параболическое, 239
— эллиптическое, 239
Уравнение
— Бесселя, 255
— Буссинеска, xii, 112, 133
— — модифицированное, 135
— Бюргерса, 97, 239
— Вебера–Эрмита, 255
— Вейерштрасса эллиптическое, 8, 44,
45, 47, 49, 53, 168, 217, 228, 236,
240, 260
— Гамильтона–Якоби, xiv, 174, 176–179,
187, 189, 191
— Гарри–Дима, 98
—Гаусса
— — гипергеометрическое, 36, 169, 241,
251, 255
— — эллиптическое, 224
— Д’Аламбера, 95
— Дегаспериса–Прочези, 98
— Ермакова–Пинни, xv, 49, 213
— КПП, 106, 159
— Кадомцева–Петвиашвили, xiii, 112
— Камассы–Холма, 98
— Каупа–Купершмидта, xiii, 29, 144,
148–152
— Кортевега–де Фриза, xi, 91–94, 103,
110, 129, 144, 148
— — модифицированное, 97, 131, 137,
142
— — пятого порядка, 29, 144
— Курамото–Сивашинского (КС), ix, xi,
18, 50, 52, 57, 59, 73, 79, 96, 227
— Лиувилля, 95, 97, 239
— Риккати, 1, 37, 59, 68, 83, 101, 120,
121, 130, 138, 139, 143, 146, 153, 165,
171, 197, 213, 227, 232, 255
— — дискретное, 210
— Савада–Котера, xiii, 29, 144, 148–152
— Свифта–Гогенберга, 52
— Уитеккера, 255
— Фишера, xiii, 109, 155
— Хальфена эллиптическое, 217
— Цицейки, 239
— Шредингера
— — линейное, xv, 49, 213
— — нелинейное, x, xi, 21, 45, 94, 96
— Штурма–Лиувилля, 49, 115, 213
— Эйри, 255
— Якоби эллиптическое, 49, 53, 168, 217
— вспомогательное, 38
— дискретное, 196
— индексное, 15, 106
— квазилинейное, 98, 106
— конечно-разностное, 197
— модифицированное, 131
— полулинейное, 98
— сингулярного многообразия, 130, 134,
140, 144, 146
— синус-Гордона, 137, 138, 239
— совершенное, 147, 194
ПРЕДМЕТНЫЙ УКАЗАТЕЛЬ 279
— солитонное, 94, 96
— теплопроводности, 91, 97
— шварциана, 214
— — дискретное, 216
— эллиптическое, 10, 40, 73, 78, 79, 81,
221, 226
— — Вейерштрасса дискретное, 217
— — Якоби дискретное, 217
— — дискретное, 221
Уравнения
—Пенлеве,9
— Янга–Миллса автодуальные, 92
— определяющие, 55, 60, 64, 70, 124,
129, 130, 134, 138, 142, 147, 156, 160,
170
— усечения, 126
Условие
— диофантово, 23, 28, 29, 106
— нелогарифмичности, 16, 106
Форма билинейная, 268
Формализм билинейный, 153, 268
Формула
— аддитивная, 217, 260, 262
— нелинейной суперпозиции, 110, 119
Функция
— Вейерштрасса эллиптическая, 235,
260
— Пенлеве, xi, 9, 37
— Хальфена эллиптическая, 261
— Якоби эллиптическая, 8, 260
— классическая, 226, 233
— мероморфная, 264
— характеристическая Неванлинны, 265
— эллиптическая, xi, xv, 26, 37, 47,
53–55, 88, 159, 198, 223, 226, 238,
259, 266
Хаос, 20
Хойер, 12, 85
Часть
— дифференциальная, 114
— линейная, 1
Члены ведущие, 14, 18, 21
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