فهرست:
فصل اول
1-1 معادلات دیفرانسیل خطی و غیرخطی.. 3
1-2 تفاوتهای بین معادلات خطی و غیرخطی ...................................................... 3
1-3 معادله شرودینگر غیرخطی.. 5
1-4 معادله کورته وگ دی وری.. 12
فصل دوم
2-1 تاریخچه ............................................................................................. 31
2-2 محیط غیرخطی و پاشندگی در امواج. 39
2-3 سالیتونهای روشن، تاریک و خاکستری.. 41
2-4 پایداری سالیتون 46
2-5 برخورد سالیتون ها 48
2-6 کاربرد سالیتون ها 50
فصل سوم
3-1 مقدمه 70
3-2 روشهای حل معادلات غیرخطی 70
3-3 قوانین بقا ............................................................................................ 75
3-4-1 روش تجزیه ادومیان. 76
3-4-2 حل معادله شرودینگر غیرخطی به روش تجزیه ادمیان. 77
3-4-3 حل معادله کورته وگ دیوری به روش تجزیه ادمیان 80
3-5-1 روش اختلال هوموتوپی ....................................................................... 81
3-5-2 حل معادله غیرخطی شرودینگر با استفاده از روش اختلال هوموتوپی ............... 83
3-5-3 حل معادله کورته وگ دی وری با استفاده از روش اختلال هوموتوپی ............... 84
3-6-1 روش تکرار تغییرات ........................................................................... 85
3-6-2 حل معادله شرودینگر غیرخطی به روش تکرار تغییرات.................................. 87
3-6-3 حل معادله کورته وگ دی وری به روش تکرار تغییرات ................................ 87
فصل چهارم
4-1 جمعبندی و ارائه نتایج ............................................................................ 92
4-2 پیشنهادات ........................................................................................... 93
پیوستها
پیوست الف (حل معادله به روش ADM) .................................................. 95
پیوست ب (حل معادله به روش HPM) ................................................. 103
پیوست ج (حل معادله به روش VIM) ................................................... 111
پیوست د (حل معادله به روش ADM) .................................................. 119
پیوست ه (حل معادله به روش HPM) .................................................. 127
پیوست و (حل معادله به روش VIM) ................................................... 135
منابع
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